上海民办新竹园中学2017学年第二学期期末测试卷(学生版)(1)

新竹园中学2017学年第二学期英语学科八年级期中考试卷上海民办新竹园中学2017学年第二学期英语学科八年级期中考试卷Part 2 Phonetics, Grammar and VocabularyII. Choose the best answer (12%)1. Choose the word that does not belong to the group.A. Good memory is important in our life.B. Ben often has sports to keep fit.C. She disappeared down the corridor.D. I often order some chocolate on the Internet2. Many important questions about the environment__________ over the past five years.A. have been risenB. were risenC. were raisedD. have been raised3. There was no bus in that small town. We had__________ walk.A. nine milesB. a nine-mileC. nine mile'sD. ninth mile4. He has always been in good health__________ he has had a slight headache in the past few days.A. besidesB. except forC.in additionD. except that5. You have kept working for two hours. You__________ tired.Have a cup of tea, please.A. must beB. may beC. maybeD. can be6．He denied__________ known anything about their plans.A. to haveB. to havingC. had D．having7.It'sreported that__________ accidents were caused by careless drivers last year.A. quantities ofB. a huge amount ofC. a lotD. the large number of8.When I got to the hall, the meeting__________ for five minutes.A. has begunB. had begunC. had been onD. has been on9. Professor Nick wanted to know__________A. when would the conference beginB. when the conference would beginC. when will the conference beginD. when the conference has begun10. They are_________ children and they have made_________ progress.A. so clever; so manyB. such clever; such muchC. so clever, such muchD. such clever, so much11. Unlike Chinese, the Europeans__________ their meals with knives and forks.A. use to haveB. are used to havingC. are used to haveD. are used for having12. -Would you mind turning off the electric fan? ---__________A. Yes, please.B. That's all right.C. Sorry, but it's too hot here.D. That's a good idea.CDBDADACBDBCIII. Complete the following passage with the words in the box, Each can only be used once. (5%)A. untilB. thinkingC. hardlyD. hadE. for herself F expectJoan worked in a hospital as a nurse. One evening there was a big dance at the hospital. Most of the doctors and nurses would be there, but of course some_____1_____ to be left to look after the children. and Joan was riot one of the lucky ones who were free to go to the dance.She liked dancing very much, so when she had to start work that eveningwhile her friends were getting ready to the dance, she felt very sorry_____2_____She went to sick children one after another and said good-night_____3_____ she came to one little boy, whom she was very fond of. His name was Dicky, and he was 11 years old, but he already talked like an adult. Poor Dickey had a very serious illness, and now he was_____4_____ able to move any part of his body except his hands. Joan knew he would never get any better, but he was always happy and always _____5_____ about other people instead of about himself.DEACBW. Fill in the blank with a proper word (7%)1, Any solution must be__________ all sides. (accept)2. She is full of__________ for the headmaster and all the teachers, (admire)3. Mary is always cruel and__________ towards he employees. (consider)4, I know that diligence is one of the most important__________ for learning.(require)5. The pilot glided__________ down to the landing-field. (skill)6. Officials said none of the__________ the plane crash was found. (survive)7. Many people believed it was his shyness and_________ which made him a strange man.(secure) Acceptable admiration inconsiderate requirements skillfully survival insecurity V. Rewrite the sentence as required (6%)1.My classmates didn't think there would be an outing the next day．（改成反义疑问句）2．She starts from home at 7:30 every morning.（保持句意不变）3．"What's the trouble with you?' The policeman asked little Peter.（改成宾语从句)4．The words on the blackboard are very small. I can't see them clearly.(合并成一句简单句) 5．His mother had him stay at home on school nights,（改成被动语态）．6. school, his mind, a, has, he, to, so as to, made up, to, study, better, hard, go1.did they2.sets off/ out3. The policeman asked little Peter whatwas the trouble with him4. The words on the blackboard are too small for me to see clearly5. He was had to stay at home on school nights by his mother6.He has made up his mind to study hard so as to go to a better schoolPart 3 Reading and WritingVI. Reading comprehension(30%)A. Read the passage and choose the best answer.(6%)Five days after the London marathon, when the hard experience and muscle ache were just memory for every other runner, Lloyd Scott, a cancer survivor, lumbered across the finish line in his deep-sea diver’s suit to a hero’s welcome yesterday.Cold, heavy, wetLloyd was interviewed by reporters from BBC and he introduced his difficult experience of his unforgettable London marathon. “During the time I’m walk ing, I have to pay att ention to a greatdeal. Although I used to be a firefighter, I can’t get used toputting on the cold, heavy, wet deep-sea diver’s suit to run the marathon. At such bad moments, I think of the money I’m raising for Clic which provides a service for children and families. But the hardest thing happens exactly each morning. When I wake up, I have to find out what hurts and how much. You can not imagine how hard it is to get into the cold and wet diving suit with all your muscles cold and having to think about what will happen next, because I also have very poor eyesight and cannot see the broken stones on the roadside.”Excellent examplePaul Simons, an officer, thinks Lloyd has demonstrated a very British sense of determination. He describes Lloyd as an excellent example to all the nation, who has a unique part of British character that the whole people need. Karen Sugarman, another fundraiser of Clic thinks of Lloyd as Superman and an inspiration to many of the sufferers throughout the UK.Years ago, Lloyd was diagnosed with cancer, he told himself it was not his end. He has come through that darkest period and he hopes that this run will encourage anyone else not to give up hope.As a cancer survivor, Lloyd Scott is a mixture of fundraiser and inspiration. He is serious about his charity work for Cancer and Children Care. He really did something “larger than life” that is very close to his heart. He once ran across the Jordan Desert dressed as Indian Jones, climbed the Everest and walked to the South Pole… and this time his London marathon run successfully won him a place in the record books for the slowest ever marathon.1. Lloyd Scott worked as a _______ before he became ill.A. doctorB. firefighterC. deep-sea diverD. marathon runner2. Lloyd Scott wore deep-sea diving costume during the race because he wanted to _____.A. see the road clearlyB. dive in the deep-seaC.raise money for charity ClicD. enjoy the running3. The underlined word ’demonstrated’ in the passage probably means.A.provedB. decoratedC. deliveredD. protected4.When he was diagnosed with cancer, Lloyd Scott .A.thought it was the endB. felt depressedB.didn’t give up D. lumbered home5. Which of the following statements is NOT TRUE according to this passage?A. Lloyd hoped to raise money for sick children.B. Lloyd met the race’s fastest man at the end of the race.C. Lloyd had poor eyesight.D. Lloyd was in pain during the race and found it very hard.6. From the passage we know Lloyd Scott ______.A.was no longer troubled by cancer.B. drove to the South Pole by himselfC. ran across the Jordan desert in his deep-sea diver’s suitD. recorded the slowest time for a marathonBCACBDB. Choose the words or phrases and complete the passage(6%)Many people would say the arts are nice, but not necessary. In school, students should focus on languages, math and science. Painting, drama and music are frills. After graduation, listening to Mozart won't lead you to a better-paying job. Not everyone needs to experience Shakespeare or Picasso to have a good life. Besides, who has time?In truth, spending time learning to appreciate the arts may be more worthwhile than you think.A recent British study examined the salaries and jobs of people who spent time enjoying the arts when growing up. The researchers found those who enjoyed the arts from an early age had better jobs and higher salaries than those who didn't. It turns out that the arts help us develop many useful skills.Other students have found students studying the arts exercise their reasoning ability．The skill helps with problem-solving．Creative and critical-thinking abilities are also developed through art study．The best kind of art stirs our imagination and makes us think．Paintings aren't just pretty pictures．They tell stories about the lives of the subjects or about the experience of the painter．Look at the world from Picasso's point of view，and you see everyday life in new ways．In Shakespeare’s plays you will find lessons about some characters. Chinese poet Li Bai brings the wonder ofnature’s beauty toe every reader.The arts help cultivate the ability to see things from different points of view. These things help us better communicate andcooperate with other people．Creativity, persistence, understanding and empathy are all qualities of successful people. If you want to better yourself，go and enjoy the arts．Check out an art gallery or a museum．Take in a play．You won't regret it and it will do you more good than you can realize.( )1. give B. offer C. lead D. bring( )2. bringing up B. growing up C. setting up D. standing up ( )3. developed B. disappeared C. decided D. described( )4.A. in B. on C. at D. with( )5. A. best B. better C. well D. more( )6. A. realize B. remember C. remind D. regretCBAABDC. Read the passage and fill in the blanks with proper words(7%)The most important thing to keep in mind when d______ to serve others is that service expects no rewards. When you expect something in return and are not sure serving out of the goodness of your heart, others will n_______. Sure they'll thank you, but the service becomes more of a situation. "I'll do this for you if you do this for me.”When you give from your heart, the real power of service comes into play. Serving is a great opportunity to strengthen your trust and r______ for another, and for them to do the same to you. Not only do you feel great about helping out but you build your relationship with them, and they feel more willing to help you in the future it's a win-win s_______.However why is service so rarely seen these days? The problem is there is always an e______ not to serve. Sure, living in this day and age does not leave us much time, and the last thingpeople want to do is work ."I’m too busy. ""it's too much work, or "I don't have the time. "may run through your head when you hear the word' service" but the truth is that the b______ are worth the sacrifice. ( 牺牲) Gandhi once said, "The best way to find yourself is to l______ yourself in the service of others. "Service is simple. Some ideas of places you can serve are volunteer centers homes, and so on.Overall, service and selfless giving to others is very powerful and has many advantages Notonly do you feel better about making other 's day a little less stressful, you can also get along with them better and they will help you more in the future.KEYS: 1.deciding 2.notice 3.respect 4.situation 5.excuse6.benefit7.lostD. Answer the questions. (11%)You must have heard a lot about the Expo volunteers. Though you really want to be a volunteer of some kind, you might not know where to start. But if you browse the Internet carefully, you will find a variety of voluntary programs waiting online.For middle school students a good beginning can be volunteering in communities. You can either work on beautifying the environment by planting more greenery or helping your neighbors by doing clean-up work or babysitting. If you are bookworm, being a community librarian may be the best choice for you. Make sure the readers obey the library rules, and then you can enjoy your favorite books for the rest of time.When you grow older, try to volunteer for some groups or organizations. Global V olunteer Network(GVN) is a good place to start GVN is a web page which provides internationalvoluntary programs. If your English is good enough, you can apply for the program of teaching little kids English.What's more, you can even try to establish your own volunteer organization. You can lead a group of people who want to help the needy as much as you do. Tan Xioyun, a 20-year-old university student, is among the young volunteer leaders. She set up her volunteer organization call "Angel Heart"when she was only 16. Now "Angel Heart has over 5000 members who are willing to do voluntary service for old people's homes and sunshine houses throughout Shanghai. So trust yourself and try your best to help make the world a better place. If you think you can, you can.1. What can middle school students do to begin volunteering?2. If you are a book worm and want to be a volunteer, what is the best choice for you?3. What is Global V olunteer Network?4. If your English is good, you can 't apply for the program of teaching little kids English, can you?(1)5. What do the members of“ Angel Heart”do?6. What volunteer work would you like to do? Why ?(at least two reasons)KEYS:1.They can volunteer in communities2.Being a community librarian.3.GVN is a web page which provides international voluntary programs.4.Yes.I can.5.They are willing to do voluntary service for old people's homes and sunshine houses throughout Shanghai.6.I would like to be a community librarian. Because the libraryis quite and I want to enjoy my favourite book alone.VIL. Translate the sentences into English(8%)1.我意识到生命多么珍贵和脆弱,我觉得我们应当珍惜我们的生命让生命中的每一分钟都有价值(cherish)2.特洛伊人在确信所有城门都已紧锁之后,就全都入睡了,包括城门的守卫。

上海民办新竹园中学2017学年度第二学期九年级英语学科考7试卷Part Ⅱ Vocabulary and GrammarⅡ. Choose the best answer (20%)Which of the following underlined parts is different in pronunciation from others?【A】contact【B】manage【C】captain【D】escape【答案】DThe young engineer solved the problem in unusual way.【A】a【B】an【C】the【D】/【答案】BSeveral thieves broke the bank and stole the safe last night.【A】into【B】down【C】out【D】off【答案】AWe saw a couple of laptops, but of them was really what we wanted.【A】neither【B】all【C】both【D】either【答案】ASteven asked the taxi driver to driver a little because he had to catch the last train.【A】quickly【B】the most quickly【C】more quickly【D】lees quickly【答案】CYou’ll not make any progress you get rid of your bad habit of study.【A】because【B】after【C】if【D】unless【答案】DTim’s sister as a waitress in a big restaurant for the time being.【A】was working【B】worked【C】has worked【D】is working【答案】DThe lawyer by a few reporters when he appears in the hall this afternoon.【A】will be interviewed【B】has been interviewed【C】is interviewed【D】was interviewed【答案】Agreat fun it is to go fishing in the countryside at the weekend!【A】How【B】What【C】What s【D】What an【答案】BThis notebook be Tom’s. Look at his name on the cover.【A】must【B】mustn’t【C】can【D】can’t【答案】AWhen the boy lost his balance, the skateboard went one way and he went .【A】the other【B】others【C】other【D】the others【答案】ADo you know the boy under the big tree?【A】lay【B】lain【C】laying【D】lying【答案】DWe our national flag every morning when the sun .【A】raise… is risen【B】rise… is raised【C】raise… is rising【D】rise… raises【答案】CPeople rarely thought of planting more trees to prevent the land from disappearing, ?【A】didn’t they【B】did they【C】do they【D】don't they【答案】BYou tired. You should get some rest.【A】hear【B】sound【C】listen【D】listen to【答案】BIf you enjoy American stories, you’ll find that quite of them take place on the road.【A】few【B】a few【C】little【D】a little【答案】BThe suspect’s friend denies him destroy evidence.【A】help【B】helped【C】helping【D】to help【答案】CBig TV’s aren’t popular today most people watch shows on their phones.【A】even if【B】so that【C】because【D】as long as【答案】C------ Hello, Jenny, you look busy. Anything I can do for you?------ I can manage myself.【A】Not at all.【B】That’s great.【C】Not at all.【D】Don’t mention it.【答案】C------ I will be away for a while. Would you mind looking after my luggage?------ .【A】Never mind.【B】That’s great.【C】Not at all.【D】Don’t mention it.【答案】CSwitzerland, you can taste as much chocolate as you like, also you may visit many chocolate museums. You will(1) about the history of chocolate, explore the traditions of Swiss chocolate making, and even watch the chocolate production process.If you have a lot of money, taking a chocolate train can be a good (2) . It will be a(3) journey to sit on a first-class seat, taste yummy chocolate, and visit the chocolate factory. You show no (4) in chocolate museums and chocolate trains? Well, a chocolate spa will meet your needs. You can give your whole body a chocolate treat! How sweet it is!【答案】BACD【分析】1.空缺动词，根据句意，了解巧克力的历史，了解固定搭配learn about，故选B2.空缺名词，根据句意，做一个巧克力火车可能是一个好的选择，故选A3.空缺形容词，根据句意，将会是一次极好的旅行，故选Cquiet moment out in the evening to relax with it?Tea has been an important part of daily life in China for hundreds of years. There is a (1) of tea, such as green tea, black tea, flower tea, and yellow tea. But two rising stars in China’s teacups - white tea and dark tea --- are becoming more and more (2) . Dark tea is made from rough, old tea leaves which darken to a deep brown colour during the long process. White tea, produced mostly in Fujian, is made by drying tea leaves. The local people(3) the fresh leaves out on the ground and keep them in jars after they have dried.Both dark tea and white tea have a long history in China. Dark tea and white tea are healthy drinks. Dark tea can (4) fat in the body, lower blood pressure and slow the aging process.【答案】BEAC【分析】1.空缺名词，各种各样的茶，固定搭配a variety of，故选B2.空缺形容词，根据句意，然而茶和红茶正变得越来越受欢迎, 故选E3.空缺动词，根据句意，当地的人们把新鲜的树叶铺开在地上，固搭spread out, 故选A4.空选动词，根据句意，红茶可以减少身体里的脂肪，故选CⅡ. Complete the sentences with the given words in their proper forms. (8分)1. The study shows that the first British came to live on this island in the _______ century. (twelve)2. The total _______ of the completed subway line 17 is 2016 kilometers. (long)3. To begin with some ______ ideas for a story are necessary. (base)4. The teacher asked us who the first European to ________ America was. (cover)5. Keeping pets is a ___________ and I’m sure I’ve been ready for that. (responsible)6. In this task, _________ thinking is required as well as team work among the group. (depend)7. They tried everything they could __________ do to improve the situation. (possible)8. After discussing for a whole day, they reached a _________ at last. (conclude)1.【答案】twelfth 十二世纪，序数词，去ve变成f2.【答案】length ，分析此处填名词，长度length.3.【答案】basic,分析此处填形容词，基本的basic4.【答案】discover,分析此处填动词，发现discover5.【答案】responsibility，分析此处填名词，养宠物是一个责任，responsibility6.【答案】independent，分析此处填形容词，独立的，independent7.【答案】possibly，分析此处填副词，可能地，possibly8.【答案】conclusion，分析此处填名词，词组达成共识，conclusionⅡ. Rewrite the following sentences as required. (14分)1. The students of Grade 6 have an Art and Crafts lesson on Monday. (改为否定句)The students of Grade 6 _______ _______ an Art and Crafts lesson on Monday.2. Most sportsman on the basketball team are tall and strong. (对画线部分提问)_______ do most sportsman on the basketball team _______ like?3. The weather affected our plans. (保持基本句意不变)The weather had an _______ _______ our plans4. “What did you do to the poor dog?” the lady asked her son. (改为宾语从句)The lady asked her son what he _____ ______ to the poor dog.5. Tina liked watching TV better than reading comic books when she was young. (保持基本句意不变)Tina _______ watching TV to _______ comic books when she was young.6. Mandarin, the Chinese language, is important to Chinese culture. (改为感叹句)_________ ___________ Mandarin, the Chinese language, is to Chinese culture!7. without, one, a student card, is not allowed, showing, to enter the hall (连词成句)_____________________________________________________________________1.【答案】don’t, have have是实义动词，所以需要找助动词否定2.【答案】What, look 问外貌的固定表达3.【答案】effect, on,影响的同意词组affect=have an effect on4.【答案】had, done,宾语从句考察时态，根据主句和直接引语时态，所以用过去完成时。

上海民办新竹园中学八年级下册期末物理试卷一、选择题1．下列说法符合日常生活实际的是（）A．大多数中学生的重约50N B．洗澡时适宜水温约60℃C．人步行速度约1.1m/s D．一个鸡蛋的质量约5g2．如图所示，一个小孩沿水平方向用力推一个静止在水平地面上的箱子，但箱子仍保持静止，则（）A．小孩对箱子的推力大于箱子受到的阻力B．小孩对箱子的推力等于箱子受到的阻力C．小孩对箱子的推力小于箱子受到的阻力D．小孩对箱子的推力与箱子受到的阻力的大小关系不能确定3．若物体不受任何外力作用，则该物体（）A．一定做匀速直线运动B．运动状态可能改变C．一定静止D．可能做匀速直线运动4．同学们，植树的场景还记得吗？下列现象与物理知识联系错误的是（）A．“移栽树苗”手紧握树苗干——增大压力，增大摩擦B．“水桶提水”手握提手粗大部位——增大受力面积，增大压强C．“铲子撒土”——利用了惯性D．标有“植树信息”的木签插入土中——减小受力面积，增大压强5．如图所示，两个相同的塑料药瓶，瓶口扎上橡皮膜，竖直的浸入水中，甲瓶口朝上，乙瓶口朝下，两药瓶在水里的位置相同，若甲药瓶恰好悬浮，则（）A．乙药瓶也处于悬浮状态B．乙药瓶受到的浮力更大C．乙药瓶内的气体密度大D．两药瓶内的气体压强相等6．如图，在水平调节平衡的轻质杠杆上挂有重物M、N，使杠杆在水平位置静止，下列说法正确的是（）A．M的质量比N的大B．N对杠杆的拉力比M小C．只将M向B端移一格，杠杆B端会下沉D．只将N向B端移一格，杠杆A端会下沉7．如图甲所示，在容器底部固定一轻质弹簧，弹簧上端连有一边长为0.1m的正方体物块A，容器中水的深度为40cm时，物块A刚好完全浸没在水中，容器侧面的底部有一个由阀门B控制的出水口，打开阀门B，使水缓缓流出，当物块A有2/5的体积露出水面时，弹簧恰好处于自然伸长状态(即恢复原长没有发生形变)，此时关闭阀门B弹簧受到的拉力F 跟弹簧的伸长量ΔL关系如图所示(不计弹簧所受的浮力，物块A不吸水)则下列分析不正确的是（）A．打开阀门前物块A受到的浮力10NB．物块A的密度0.6×10kg/m3C．物块A刚好完全浸没在水中时，弹簧伸长了2cmD．弹簧恰好处于自然伸长状态时水对容器底部的压强3.6×103Pa8．如图所示，小明用不同的力F1、F2，在相同时间内分别把物体A直接匀速拉升h高度，和沿粗糙斜面匀速拉升h高度。

上海民办新竹园中学2017学年度第二学期九年级英语学科考7试卷（考试时间100分钟，满分150分）Part1 Listening（第一部分听力）（共30分）A. Listen and choose the right picture.（共6分）1.________2. ________3. ________4. ________5. ________6. ________B. Listen to the dialogue and choose the best answer to the question you hear. (8分）7. A. A doctor. B. A detective C. A policeman D. A postman8. A. Buy a new purse. B. Call the police C. Repair her purse D. Look for her purse9. A. He was sunbathing with Peter. B. He was bathing in the bathroomC. He was playing basketball with PeterD. He was playing tennis with Peter.10.A. At1:00 B. At1:30. C. At2:30 . D. At3:30.11.A. A detective. B. A reporter. C. An actor. D. A writer.12.A. $ 5,750 B. $5,850 C. $ 5,950 D. $ 6,40013.A. Sales B. Nurses. C. Teachers D. Tourism managers14.A. 1,000 dollars B. 1,100 dollars C. 1,200 dollars D. 1,300 dollarsC. Listen to the passage and tell whether the following statements are true or false.（6分）15.In the story, Kuskoy is the name of a country.16.The children of Kuskoy begin to learn to whistle（（吹ロ哨）at school.17.In Kuskoy, whistling as a way of talking started hundreds of years ago.18.The whistle can be heard at a distance of 10 miles.19.The children of Kuskoy always start a day with a whistled song.20.Through whistling, all the villagers quickly knew a young-couple’s adventure.D. Listen to the passage and complete the following sentences.（10分）21.Mr. Bram became completely blind ________ ________.22.Mr. Bram graduated with a degree ________ ________ although his condition was declining all the way.23.M. Bram picked up a bottle of glue and drew cutlines that he could feel with ________ ________24.Mr. Bram once said that he didn’t become ________ ________ to fail until he lost his sight.25.Mr. Bram learnt that he should live in the moment and________ ________through stressful situations from painting.Part 2 Phonetics, Grammar and vocabulary(第二部分语音、语法和词汇）II. Choose the best answer (20分)26.Which of the following underlined parts is different in pronunciation from others?A. contactB. manageC. captainD. escape27.The young engineer solved the problem in________unusual wayA. aB. anC. theD. /28.Several thieves broke ________the bank and stole the safe last night.A. intoB. downC. outD. /29.We saw a couple of laptops, but________of them was really what we wanted.A. neitherB. allC. bothD. either30.Steven asked the taxi driver to driver a little________because he had to catch the last train.A. quicklyB. the most quicklyC. more quicklyD. less quickly31.You’ll not make any progress ________ you get rid of your bad habit of study.A. becauseB. afterC. ifD. unless32.Tim's sister________as a waitress in a big restaurant for the time being.A. was workingB. workedC. has workedD.is working33.The lawyer________ by a few reporters when he appeared in the hall this afternoon.A. will be interviewedB. has been interviewedC. is interviewedD. was interviewed34.________ great fun it is to go fishing in the countryside at the weekend!A. HowB. WhatC. What aD. What an35.This notebook________ be Tom's. Look at his name on the coverA. mustB. mustn'tC. canD. can’t36.When the boy lost his balance, the skateboard went one way and went________ .A. the otherB. othersC. otherD. the others37.Do you know the boy ________under the big tree?A. layB. lainC. layingD. lying38.We________ our national flag every morning when the sun________.A. raise...is risenB. rise...is raisedC. raise...is risingD. rise... raises39.People rarely thought of planting more trees to prevent the land from disappearing,________?A. didn’t theyB. did theyC. do theyD. don’t they40.You________ tired. You should get some rest.A. hearB. soundC. listenD. listen to41.If you enjoy American stories, you’ll find that quite________of them take place on the road.A. fewB. a fewC. littleD. a little42.The suspect's friend denies________ him destroy evidence.A. helpB. helpedC. helpingD. to help43.Big TV's aren’t popular today________ most people watch shows on their phones.A. even ifB. so thatC. becauseD. as long as44.---Hello, Jenny, you look busy. Anything I can do for you?--- ________I can manage myself.A. Not at allB. I'm afraid notC. Thank you all the sameD. All right45.--- I will be away for a while. Auld you mind looking after my luggage?--- ________ I can manage myself.A. Never mind.B. That's great. C Not at all. D. Don’t mention it.III. Complete the following passage with the words or phrase in the box. (8分)No matter whether you have a sweet tooth or not, you can't miss tasting Swiss chocolate. In Switzerland, you can taste as much chocolate as you like, also you may visit many chocolate museums. You will 46 about the history of chocolate, explore the traditions of Swiss chocolate making, and even watch the chocolate production process.If you have a lot of money, taking a chocolate train can be a good 47 . It will be a 48 journey to sit on a first-class seat, taste yummy chocolate, and visit the chocolate factory.You show no 49 in chocolate museums and chocolate trains? Well, a chocolate spa will meet your needs. You can give your whole body a chocolate treat! How sweet it is!Do you love to start your day with a cup of tea in the morning? Maybe you enjoy taking a quiet moment out in the evening to relax with it?Tea has been an important part of daily life in China for hundreds of years. There is a 50 of tea, such as green tea, black tea, flower tea, and yellow tea. But two rising stars in: Chinas teacups --- white tea and dark tea --- are becoming more and more 51 . Dark ta is made from rough, old tea leaves which darken to a deep brown colour during the long process. White tea, produced mostly in Fujian, is made by drying tea leaves. The local people 52 the fresh leaves out on the ground and keep them in jars after they have dried.Both dark tea and white tea have a long history in China. Dark tea and white tea are healthy drinks. Dark tea can 53 fat in the body, lower blood pressure and slow the aging process.IV. Complete the sentences with the given words in their proper forms. (8分)54.The study shows that the first British came to live on this island in the ________century. (twelve)55.The total ________ of the completed subway line 17 is 2016 kilometers.(long)56.To begin with some -basic ideas for a story are necessary.(base)57.The teacher asked us who was the first European to ________America. (cover)58.Keeping pets is a ________ I’m sure I’ve been ready for that. (responsible)59.In this task, ________ thinking is required as well as team work among the group. (depend)60.They tried everything they could ________ do to improve the situation.(possible)61.After discussing for a whole day, they reached a ________at last. (conclude)V. Rewrite the following sentences as required. (14分)62.The students of Grade 6 have an Art and Crafts lesson on Monday．（改为否定句）The students of Grade 6 ________ ________an Art and Crafts lesson on Monday63.Most sportsmen on the basketball team are tall and strong.（对画线部分提问）What do most sportsmen on the basketball team ________like?64.The weather affected our plans.（保持句意基本不变）The weather had an ________ ________our plans.65.“ What did you do to the poor dog？” the lady asked her son.（改为宾语从句）The lady asked her son what ________ ________to the poor dog.66.Tina liked watching TV better than reading comic books when she was young.（保持句意基本不变）Tina ________ watching TV to ________comic books when she was young.67.Mandarin, the Chinese language, is important to Chinese culture（改为感叹句）________ ________Mandarin, the Chinese language, is to Chinese culture!68.without, one, a student card, is not allowed, showing, enter the hall（连词成句）______________________________________________________________________Part3 Reading and Writing（第三部分读写）A. Choose the best answer. (12)Linxi had taken part in a 6-month international student exchange scheme to Britain. When she came back, she wrote an article about the impression of Britain for the school newspaper. The following are parts of her article：Personal SpaceBritish people like a lot of space around them. They don’t like to make physical contact of any kind with strangers and feel very uncomfortable if anyone stands too close to them. One example of the British ‘keep their distance’ is that people do not often shake hands with one another at all.Making Polite RequestIn making polite requests, British people like to use very indirect language, using the conditional tense and negatives. Amita, an Indian student said: ‘British people never got to the point. They go around this way and that way, using twenty words where three would do. It's really hard to communicate with them.’ (David! British High School Official gave his comment: ‘Some nationalities do not always seem very polite; ‘I want this’ or ‘I want that’, no smiles nor a please nor a thank you.’SmilingSome students say that British people smile a lot, compared to many national groups--- often for no particular reason. The British smile as a greeting, smile when asking for something, smile on receiving it.King, a Korean student once said: ‘The British are so insincere. They smile even when they are not happy or pleased to see you. One girl smiled at me every time we passed each other and I thought she really liked me. So I asked her to come out with me and she refused. She was leading me on and then turned me down.’ Well, she maybe did not realize that she was smiling and probably smiled at everyone. But it is easy to see how this could be misinterpreted by someone in whose culture smiles are only to express genuine warmth.But still many students comment that they do not find British people in shops, banks, at reception desks smile enough to make them feel welcome.69.British people need a lot of space around them, so they ________.A) make physical contact with others B) stand close to other peopleC) don’t often shake hands with others.D) don’t like strangers70.To make polite request, British People________.A) say directly what they need B) say indirectly what they needC) use less words than necessary D) use very polite words71.According to David,________.A) British people are not polite enough B) British don't like people of other nationalitiesC) it is important to use please "and 'thank you' D) people from other countries always smile72.King thought British people are not sincere because they________.A) smile to show refuse B) smile at people they are not pleased to seeC) smile to show politeness D) smile at everyone73.The underlined word "misinterpreted" in this passage probably means ________.A) understood correctly B) understood wronglyC) expressed easily D) expressed difficultly74.The best title for Linxi's article may be________.A) The British in My Eyes B) Always Be PoliteC) Students From Different Counties D) Polite British PeopleB. Choose the words or expressions and complete the passage. (12分)What makes people different from computer programs? What is the missing element that our theories don’t yet account for? The answer is simple: People read newspaper stories for a reason: to learn more about what they are interested in. Computers, on the other hand don’t.75 , computers don’t even have interests; there is nothing in particular that they are trying to find out when they read. If a computer 76 is to be a model of story understanding, it should also read for a “purpose”.Of course, people have several goals that do not make 77 to attribute to computers. One might read a restaurant guide in order to satisfy hunger or entertainment goals, or to 78 a good place to go for a business lunch. Computers do not get hungry, and computers do not have business lunches.However, these physiological and social goals give rise to several intellectual or cognitive(认知)goals. A goal to satisfy hunger gives rise to goals to find information about the name of a restaurant which 79 the desired type of food, how expensive the restaurant is, the location of the restaurant, etc. These are goals to get information or knowledge, which we are calling 80 goals. These goals can be held by computers too; a computer might “want” to find out the location of a restaurant, and read a guide in order to do so in the same way as a person might. While such a goal would not arise out of hunger in the case of the computer, it might well arise out of the “goal” to learn more about restaurants.75.A. However B. In addition C. In fact D. Instead of76.A. program B. instruction C. system D. function77.A. success B. sense C. scene D. point78.A. find B. go C. look D. watch79.A. orders B. create C. supports D. serves80.A. understanding B. learning C. feeling D. awarenessC. Read the passage and fill in the blanks with proper words.(14分)Number 1 is the simplest number, but has the most complex cultural meaning in Chinese culture. It has the meaning of the beginning, the origin, and the whole w81 was first suggested by Lao Zi, a well-known philosopher in ancient China in his classic text-TaoTe Ching. Meanwhile, this number was r82 as “the mother of all creatures” by some other Chinese philosophers in ancient times. Chinese people respect it for its meaning of the first and winner the s83 as in Western culture. It is easy to find how people love the word from Chinese ancient literature. There are over 260 phrases and more than 420 idioms b84 with this word in Chinese language system. In Chinese culture, it is n85 lucky nor unlucky. The combination with some other numbers has positive meanings, such as 1314. I86 pronunciation in Chinese sounds similar to lifetime or forever, which is widely used between lovers. Sometimes, I sounds similar to the word “You”. The common use of 5211314 in network language means “love you forever” 521 s87 means “I love you”, which is the most beautiful line to all.D. Answer the question. (12分)He almost didn’t see the old lady stand on the side of the road, but even in the dim light of day, he could see she needed help. So he stopped his car and got out, walked towards her.Even with the smile on his face, she was worried. No one had stopped to help the last hour or so. Was he going to hurt her? He didn't look safe.He said, “I am here to help you, ma’am. Why don’t you wait in the car where it is warm? By the way, my name is Bryan Anderson.”Well, she had was a flat tire（爆胎）, but for an old lady, that was bad enough. Bryan crawled under the car looking for the Jack, and hanged the tire. But he had to get dirty, and his hands hurt. As he was tightening up the lug nuts（螺母）, she rolled down the window and began to talk with him. She told him that she was from St Louis and was only just passing through. She was grateful for his help.Bryan just smiled as he finished the work. The lady asked how much she owed him. Any amount would have been all right with her. She already imagined all the awful things that could have happened if he had not stopped. Bryan neverthought about being paid. This was not a job to him. This was helping someone in need, and God knows there were plenty who had given him a hand in the past. He had lived his whole life that way, and it never occurred to him to act any other way.He told her that if she really wanted to pay him back, the next time she saw someone who needed help, she could give the person the assistance he or she needed, and Bryan added, ""And think of me.He waited until she started her car and drove of It had been a cold and depressing day, but he felt good as he headed home disappearing into the twilight.88.Why did the old lady stand on the side of the road?(2’)_______________________________________________________________________89.The old got no help before she met Bryan, did she?(1’)_______________________________________________________________________90.What, wrong with the old lady's car? (2’)_______________________________________________________________________91.How did Bryan help the old lady with the car? ( 2’)_______________________________________________________________________92.Why didn’t Bryan ask the old lady to pay for what he had done for her? (2’)_______________________________________________________________________93.If you meet a stranger who is in trouble, will you help him/her Why? (give 2 reasons)(3’)_______________________________________________________________________VII. Writing（20分）In 60 to 120 words, write about the topic “... is a good habit”.（以“…是好习惯”为题，写一篇60-120个词的短文，标点符号不占格）一个好的习惯会让我们终生受益。

上海民办新竹园中学2017学年第二学期英语学科九年级考10试卷Part 1 Listening (第一部分听力)I.Listening Comprehension (听力理解)(共30分)A．Listen and choose the right picture（根据你听到的内容，选出相应的图片）：（6分）1.________2.________3.________4.________5.________6._______B.Listen to the dialogue and choose the best answer to the question you hear.(根据你听到的对话和问题，选出最恰当的答案) (8分)7.A)Jim. B)Jenny. C)Lily D.Linda8.A)A TV play B) The TV news C)Their past D)Their hometown.9. A)By asking for them from a friend. B)By lining up in front of the ticket officeC)By booking them on the phone D)By buying them from someone else10. A)He had lost Mr. Smith's dictionaryB)He had forgotten to bring Mr. Smith' s dictionary.C)He had forgotten to give Mr. Smith the dictionaryD)He had forgotten to tell Mr. Smith to bring the dictionary.11. A)In a bookshop. B)In a library. C)In a hospital D) In a store12. A)Eight hours B)Six hours C)Three hours D)One hour.13. A )After one o'clock. B)Before twelve o'clock.C)Before one o'clock. D)At a quarter past twelve.14. A)Mother and teacher B)Mother and sonC)Father and teacher D)Teacher and studentC.Listen to the passage and tell whether the following statements are true or false(判断下列句子是否符合你听到的短文内容，符合的用“T”表示，不符合的用“F"表示)（共6分）15.John Slack went to Royal Hotel to book a room.16.He needed a single room or the 15th of October room17.He wanted to enjoy the beautiful lake view in the room.18.He must pay $840 for his stay in the hotel with breakfast.19.He can check in at 12:30 pm when he arrives at the hotel. %.20.This dialogue is mainly about how to book a hotel roomD. Listen to the passage and complete the following sentences(听短文,完成下列内容,每空格限填一词):(共10分)21.Let me tell you stories of great animal parers.22.After the heavy rain, a dog swam to an island .23.The mother dog swam to the island every day to feed .24.Chimpanzees (a )also cared for those that got lost.25.The brave parents rushed down to the road and took the bird away.Part 2 Phonetics, Grammar and Vocabulary(第二部分语音、语法和词汇)I.Choose the best answer(选择最恰当的答案):(共20分)26.Which of the following underlined parts is different in pronunciation from the others?A)You will be able to read in peace B)Shall I ask for a large steak?C)Ice cream is high in fat and sugar. D)Who is weak in spelling in class?27.Spring Festival is wonderful time for people to visit friends and relax.A)a B)an C)the D)/28.The charity walkers arrived at the small town a rainy morning.A)in B)at C)on D)of29.This match provides us _________ an excellent chance to try out some new players.A)from B) about C)for D) with30.More than half a million British people have a second home in .A)other B)the other C)another D) others31.can learn how to surf the Internet safely and effectively in computer lessons in other country.A)You B)Your C)Yours D) Yourself32.Doing eye exercises is one of ways to protect your eyes.A)good B)better C)best D) the best33.He looked at the young man and couldn’t say a word.A)friendly B)angrily C)lonely D)lovely34.Would you like the sunshine on the beach with me?A)enjoy B)enjoying C)to enjoy D) enjoyed35.Peter keeps us he’s going to be a famous artist before he’s 40.A)tell B)telling C)to tell D)told36.you lend me your spare pen？I have left mine at home.A)May B)Should C)Must D)Could37.I your email after the meeting and see whether it’s there or not.A)will check B)am checking C)have checked D)checked38.Paul failed his driving test because he enough before.A)wasn’t practising B)doesn’t practise C)hadn’t practised. D)wouldn’t practise39.People to send up fireworks around the centre of the city last Spring FestiveA)weren't allowed B)won't be allowed C)are not allowed D)haven’t been allowed40.I like reading, I always spend my pocket money on books.A)for B)but C)so D)or41.George will soon fall behind he finds a better way and applies it to practice.A)because B)when C)until D)unless42.The school aims to encourage people to take a full part in society, it?A)is B)isn't C)does D)doesn't43.-- woman is your English teacher?-- The woman in a red skirtA)Who B)What C)Which D) Whose44.-- .--Sorry. She isn't at home nowA)May I speak to Linda? B)Are you Linda?C)Do you know Linda? D)Can I help you, Linda?45.-- I feel so nervous about the English Speech Competition tomorrow.-- .A)That's cool B) Take it easy. C)Sounds great. D)Glad to hear thatIII. Complete the following passage with the words or phrases in the box. Each word or phrasecan only be used once(将下列单词或词组填入空格。

上海民办新竹园中学物理八年级下册期末试卷含答案一、选择题1．下列物理常识，说法正确的是（）A．托起两个鸡蛋的力大约是1NB．一个中学生所受重力大约是45﹣70NC．我们当地的大气压强约为1000 PaD．一个标准大气压可支持的水柱高约为760 mm2．如图甲、乙所示，桌上有两个相同的杯子，杯中装有等量的水，取两个相同的空药瓶，瓶口扎上两块完全相同的橡皮膜，用竖直向下的外力使他们竖直地浸入水中相同位置，甲杯中瓶口朝上，另一个瓶口朝下。

下列说法中正确的是（）A．甲图中水对药瓶的浮力小于药瓶的重力B．乙图中水对药瓶下表面的压力与药瓶的重力是一对平衡力C．乙图中橡皮膜凹陷程度比甲图中橡皮膜凹陷程度大D．乙图中药瓶受到的浮力比甲图中药瓶受到的浮力大3．如图所示，各图与相应描述相符的是（）A．排球被接起后，竖直上升到最高点时受到的合力竖直向下B．跳水运动员能够起跳，是因为跳板对她的作用力大于她对跳板的作用力C．空中飞行的实心球突然不受力时，将继续保持曲线运动D．运动员举起杠铃时，地面对运动员的支持力和运动员受到的重力是一对平衡力4．下列事实中，目的是为了增大压强的是（）A．篆刻刀的刀口做得很锋利B．铁轨下面铺放枕木C．推土机用宽大的履带来支承D．载重汽车有很多轮子5．某同学将一支自制的简易密度计放人盛有不同液体的两个烧杯中，静止后的情形如图所示，两液面相平｡下列判断正确的是A．密度计在甲液体中受到的浮力比在乙液体中受到的浮力小B．甲液体对容器底部的压强比乙液体对容器底部的压强小C．密度计越靠上的刻度，对应的密度值越大D．甲液体的密度比乙液体的密度大6．如图所示，杠杆的两侧挂有钩码，处于水平位置平衡状态。

接下来的一些操作，仍能使杠杆保持水平位置平衡的是（）A．两侧钩码同时向外移一格B．两侧钩码同时向内移一格C．左侧的钩码向外移一格，右侧减去一个钩码D．左侧减去一个钩码，右侧的钩码向内移一格7．如图所示，相同体积的四个小球放在盛有水的四个相同容器中保持静止．C球对容器底有压力，D球上的细线处于拉伸状态，四个容器中的水面到容器底的深度相同，四个容器中对桌面产生的压强相等的有（）A．1 个B．2 个C．3 个D．4 个8．某型号电动车自重为600N，行驶时速最高可达36km/h，车轮与地面的接触总面积为200cm2，车胎能承受的最大压强为2.3×105Pa，若该车以最高时速匀速行驶2h，受到的阻力为40N，下列说法中（）①该车的最大载重量4600N②该车最高速行驶时输出功率为400W③该车行驶了72km④该车克服摩擦力做的功为2.88×104JA．只有②③正确B．只有①④正确C．只有②③④正确D．①②③④都正确二、填空题9．如图所示，图甲、乙分别反应了力的作用放果，其中甲图表示力可以改变物体的____________；乙图表示力可以改变物体的____________。

MBA 2017—2018学年上海市浦东新区民办新竹园中学八年级下学期期中考试卷一、填空题（每空2分，满分30分）1、已知直线b x y +-=23经过点()()12,2,,1A m B m --两点，则1m 2m【答案】＞2、已知一次函数b kx y +=的图像经过点（1，-2），且不经过第三象限，那么关于x 的不等式2>+b kx 的解集是【答案】x ＜1 3、方程021=-•+x x ）（的根是【答案】x =24、用换元法解分式方程02232=----x x x x 时，如果设y xx =-2，则原方程可化为关于y 的整式方程是【答案】032y 2=--y5、用20cm 长的绳子围成一个等腰三角形，设它的底长为y cm ，腰长为x cm ，则y 与x 之间的函数关系式为 （写出自变量x 的取值范围） 【答案】y =20-2x (5＜x ＜10)6、已知一个把多边形的内角和与外角和相加，所得的和是2160度，那么这个多边形是 【答案】127、已知一个菱形的对角线长分别为3和4，那么这个菱形的周长为 【答案】108、如图，正方形ABCD 的边长为8，M 在DC 上，且DM =2，N 为AC 上的一个动点，则DN +MN 的最小值为 【答案】10A BA 8、如图，在矩形ABCD 中，AE 平分∠BAD ，∠EAO =︒15，则∠BOE 的度数是 【答案】75°9、如图，将正方形ABCD 折叠，使点C 与点D 重合于形内点P 处，折痕分别为AF 、BE ，如果正方形ABCD 的边长为2，那么∆EPF 的面积是 【答案】12-37【提示】过点p 分别向CD 和AB 做垂线，交点分别为Q .M ，易知PM =3，可得PQ =2-3，由翻折可推∠FEP =30°，根据勾股定理可求得各个边长度即可求出面积10、在平行四边形ABCD 中，∠B 的平分线将CD 分成4cm 和2cm 两部分，则平行四边形ABCD 的周长为 【答案】20cm 或16cm 11、一次函数343+-=x y的图像分别于X 轴，Y 轴交于A 、B ，将线段AB 绕点A 顺时针旋转90度得到线段AC ，则B 、C 两点的直线解析式为 【答案】371y +=xAB12、如图，将矩形纸片ABCD 折叠，B 、C 两点恰好重合落在AD 边上点P 处，已知∠MPN =︒90，PM =3,PN =4，那么矩形纸片ABCD 的面积为【答案】5144二、选择题（本大题共6题，每题2分，满分12分） 13、下列方程不是二项方程的是（ ） （A ）02=+x x（B ）09313=+x （C ）15=x （D ）324=-x【答案】A14、方程组⎩⎨⎧=-=-ky x y x 222有实数解，则K 的取值范围是（ ）(A) 3≥k（B ）k =3 (C ) k <3 （D ）3≤k【答案】D15、下列命题中，假命题是（ ）（A ）两条对角线互相平分的四边形是平行四边形 （B ）两条对角线互相垂直的平行四边形是菱形 （C ）两条对角线相等的平行四边形是矩形 （D ）两条对角线互相垂直且相等的四边形是正方形 【答案】D 16、一次函数1+=x y的图像交于x 轴，y 轴于点B ，点C 在x 轴上，且使得∆ABC 是等腰三角形，符合题意的点C 有（ ）个 A 、2 B 、3 C 、4 D 、5CA【答案】C17、平行四边形ABCD 中，对角线AC 、BD 交于点O ，AC =10cm ，BD =8cm ,则AD 的取值范围是（ ）A 、AD >1B 、AD <9C 、1<AD <9 D 、AD >9 【答案】C18、如图，平行四边形ABCD 中，P 是图形内任意一点，∆ABP ，∆BCP ，∆CDP ，∆ADP 的面积分别为4321,,,S S S S ,则一定成立的是（ ） A 、4321S S S S +>+ B 、4321S S S S +=+B 、4321S S S S +<+ D 、231S S S =+【答案】D三、计算题（每题5分，共15分） 20、解方程：1236211212----=--x xx x 【答案】3,32x 21-==x 21、解方程:36132+=++x x x x【答案】1,3x 21==x22、解方程组：⎩⎨⎧=-+=+361322y xy x y x 【答案】11525x y ⎧=⎪⎪⎨⎪=-⎪⎩四、解答题（共47分）23、（本题9分）一个水槽有进水管和出水管各一个，进水管每分钟进水a 升，出水管每分钟出水b升，水槽在开始5分钟内只进水不出水，随后15分钟内既进水又出水，得到时间x与水槽内的水量y（升）之间的函数关系（如图所示）（1）求a,b的值（2）如果在20分钟之后只出水不进水，求这段时间内y关于x的函数解析式及定义域分析：（1）根据图象上点的坐标，可以得出水槽内水量与时间的关系，进而得出a，b的值；（2）根据在20分钟之后只出水不进水，得出图象上点的坐标，进而利用待定系数法求出即可．【答案】【解答】(1)由图象得知：水槽原有水5升，前5分钟只进水不出水，第5分钟时水槽实际存水20升。

上海民办新竹园中学2017学年第二学期英语学科初三考12试卷Part 2 Vocabulary and GrammarII. Choose the best answer (选择最恰当的答案)：（共20分）26.Because it was warm, David wore only a white cotton shirt. which of the following is correct for the underlinedword?A. /'kɒtn/B. /'kʌtn/C. /'kɚtn/D. /'kɔːtn/27.Susan went back home in ________ hurry as her mom had prepared ________ rich dinner.A. a, aB. the, theC. a, theD. the, a28.Many ________ victims lost their homes in the destructive earthquake that hit in Japan.A. thousandsB. thousands ofC. thousandD. thousand of29.[ knowledge can be found in an encyclopedia.A. huge amounts ofB. a number ofC. quite a fewD. quite many30.You may go to Shanghai Animal Zoo by ________ of the two waysA. bothB. eitherC. everyD. all31.To achieve noticeable improvements, you’d better ________ much time on recreation.A. spendB. to spendC. not spendD. not to spend32.Junior three students feel excited about having a________ holiday after the high school entrance examinations.A. three-month’sB. three-monthC. three month’sD. three-months33.________ sad news it is that Syria suffered great loss and damage after the air strikes launched by the US, Franceand the UK!A. WhatB. What aC. HowD. How a34.Nowadays, children under 1.4 metres ________ be free to take buses in some cities.A. needB. shallC. canD. must35.Why did the patient refuse ________ the medicine?A. takingB. to takeC. takenD. take36.The waiter talked as ________ he could to make the customers understand her.A. clearB. clearerC. clearlyD. more clearly37. A student will achieve nothing ________ he himself devotes all his energies to learning.A. ifB. unlessC. sinceD. when38.E-mail, as well as telephones, ________ an important part in daily communication.A. are playingB. have playedC. is playingD. play39.--Kitty, why are you still here? The speech contest has begun.--I am sorry, but I ________ when to begin.A. don’t tellB. didn’t tellC. haven’t toldD. wasn’t told40.“ ________ a bit more time on English learning and your effort won’t be in vain.” said Jenny’s teacher.A. SpendingB. To spendC. SpendD. Spends41.Let her visit the underwater hotel instead of you, ________ ?A. shall weB. will youC. will sheD. do you42.Helen was too angry to say ________ .A. nothingB. somethingC. everythingD. anything43.Fishing is an excellent hobby for a kid to ________ as it can help them to be patient.A. pick upB. take upC. turn upD. put up44.He hasn’t decided ________A. when does he book the ticket by phone in advanceB. when he would book the ticket by phone in advanceC. if he books the ticket by phone in advanceD. if he will book the ticket by phone in advance45.--Would you like me to show you around the Bund? -- ________A. Yes, I’d love toB. My pleasureC. You’re so sweetD. Yes, go aheadIII. Complete the following passage with the words or phrases in the bank. Each can be used only once．（8分）On a hot summer day in the park, I went to sit in the shade by a tree. As soon as I sat down, a man dressed in colourful clothes stood up and shouted, “Hello, ladies and gentlemen, please gather around me.” He started to46 magic tricks, with the help of people in the park.In a matter of 47 , a crowd of about 20-30 people gathered. He is what we call a street performer or busker.( 卖艺人).There are many different busker performances 48 magic, music, and dance. The list goes on. Once in Spain, I saw a street artist painting a picture of a person as he sat there 49 .The history of busking goes all the way 50 to early civilization. And so it is possible to see a street performer on the streets of any city in the world!Britain is home to a strong busking 51 And with London being Britain’s most popular tourist city, it has also becom the city for street artists. Many 52 singers and actors once were street artists, such as singer Rod Stewart, actor Eddy Izzard and former James Bond actor Pierce Brosnan. It is most probable to go from the streets to the stars.And yet, some people may dislike street performers 53 they are noisy, but they can help to brighten our day –or at least add something colorful to a boring day.46. ________ 47. ________ 48. ________ 49. ________50. ________51. ________52. ________ 53. ________IV. Complete the sentences with the given words in their proper form（8分）54.Professor Zhang will make several ________ on Chinese art during his stay in USA. (speech)55.They were proud to say these paintings belonged to ________ (they)56.For the first time since his ________ , he relaxed slightly (arrive)57.Arthur seemed ________ by the question. (embarrass)58.According the news, Food waste is caused by ________ reasons. (variety)59.The right to work is a ________ right of a citizen. (base)60.Could you name three ________ events that happened in Ming Dynasty?( history)61.Alice took up ________ in college so that she could communicate with friends in Paris. (France)V Complete the following sentences as required. (14分)62.You need to pack your clothes now. （否定句）You ________ ________ to pack your clothes now.63.This latest research has no practice use at all.（反义疑问句）This latest research has no practice use at all, ________ ________ .64.Be careful, or you will make the same mistake again.（保持句意）________ you ________ careful, or you will make the same mistake again.65.The took the wounded into a small temple at once. （被动语态）The wounded ________ ________ into a small temple at once.66.Will you take part in our English evening? Mr. Anderson asked me.（合并一句）Mr. Anderson asked me________ I ________ take part in our English evening.67.The poor child was so lucky that she got many books from project Hope.（保持句意）The poor child was ________ ________ to get many books from project Hope.68.had, newspapers, English, it, more, you, read, to, better, often, improve.（连词成句）_______________________________________________________Part 3 Reading and WritingA. Read the passage and choose the best answer(共12分)Choose the best answer.69.What do we know about Jane right before she disappeared ?A. She tried to save several other women in danger.B. She was talking to a stranger.C. She was walking to college with a friend.D. She stopped at a local shop.70.The possible reason for Arthur’s disappearance is ______.A. money problemB. family matterC. communication problemD. trouble with children71.From the underlined part about what Mrs. Sugden said, we know about ______ .A. she has already solv ed her husband’s problemB. she already knows why her husband disappearedC. she still hopes that her husband will come backD. the family knew Arthur might run away72.Dickie disappeared ______ .A. near his homeB. on his way to schoolC. on the beachD. in the sea73.According to the police, ________..A. Dickie was alone on the beach before he disappearedB. Dickie was unlikely to fall into the sea while playingC. Dickie’s brother Leon pushed Dickie over a wallD. Dickie’s father was responsible for the boy’s disappearance74.The above article is likely to appear in a ________.A. police reportB. police recordC. public noticeD. research paperB. Choose the words or expressions and complete the passage (12分)Advertisements are everywhere. The number of job advertisements has increased rapidly in the last few years. Jobs are sometimes advertised nationally and sometimes locally. Now we are going to look at some job advertisements of the type that 75 in local British newspapers. When people look at such advertisements, they are usually interested in finding a specific sort of job for themselves or for someone they know. They are unlikely to read every advertisement word by word. They glance over each one to see if it’s relevant to their n eeds and then, if it is, they go on to read it in more 76 .Have a look at the job advertisements below.Mother’s help:￡3.25 per hour, 10 hours per week between 3-6 pm Mondays to Fridays (flexible) to 77 two children from school in centre of Clifton, do domestic duties until parents arrive home: vacuuming, dusting cleaning, etc. experience and advantage. Fef.6682Care Assistant:Full and part-time posts 78 in nursing home for the elderly. Duties including assisting patients with personal care programmes and general daily living skills. Must have patient 79 . Salary negotiable (协商的). Opportunity for taking Care Assistant training course. Ref. 6414Full-time stylist for city centre salon:Must have experience in both men and women’s styling. 38 hours per week, to carry out normal duties, 80 cutting, trimming, perming（修剪） and tinting（染发）. Minimum of 4 years’ experience essential. Over 30 preferred. Wages dependent on qualification & experience. Ref.6213A75. A. appeared B. imagined C. examined D. published76. A. trouble B. detail C. danger D. surprise77. A. interview B. protect C. collect D. attack78. A. important B. equal C. available D. awful79. A. sense B. responsibility C. ability D. attitude80. A. besides B. including C. except D. plusC. Read the passage and fill in the blanks with proper words（14分）"I sometimes get up at three or four in the morning and I surf the net.""I often c 81 my e-mail forty times a day.""I often spend more than three hours during one time on the net.""I spend more time in chat rooms than with my real-life friends."Do you know any people like these? They are part of a new addiction called Internet addiction. Internet addicts spend at l 82 thirty to forty hours online every week. The use of the Internet can be an addiction like drug use. People lose control of the time they spend on the Internet. The use of Internet can be an addiction like drug use.For example, one college student was missing for several days. His friends were w 83 , and they called the police. The police found the student in the computer lab: he was surfing the net for several days straight.S 84 show that about 6% to 10% of Internet users become addicted. And people worry about the teens because the Internet is changing the playing field for some of them. They spend more time in cyberspace than in the real world of friends and family.Is "surfing the net" a h 85 or an addiction for you? You may have a problem if you have these symptoms:● You do not go to important family activities or you do not do school work because you like to spend hours on the Internet.● You can't wait for your n 86 online time. You plan to spend a short time online, but then you spend several hours.● You go out with your friends less and less.What is the s 87 ? There is advice to help Internet addicts. Some experts recommend that people set strict limits in their time for Internet use. You have to control it. The Internet shouldn’t control you.D. Read the passage and answer the questions：（12分）Playing is serious business for children. In fact, it’s what they do best! Ask them why they do it, and kids will probably say, “Because it’s fun!” But it’s much more than that. It’s also good for them.Studies show that from birth babies begin learning through play. They use their five senses to get to know their new world. Touching allows them to discover how different things feel. Brightly coloured toys and clothing help develop a baby’s sense of sight (视觉). When small children choose which toy to play with, they begin developing their abilities in making decisions.Children love toys that allow them to use their imagination (想象力). Sometimes an empty box is more fun than a high-tech (高科技) toy. That’s because a box can become anything a child imagines it to be.Crayons, paints and Play-Doh (彩色塑泥) are also good because they allow children to create. Traditional building blocks teach important pre-math skills.Playing doesn’t become any less important once children start school. Many valuable lessons about life are learned on the school playground. Kids learn how to share, take turns and play by the rules.Health officials give another good reason for why children should play. Kids need exercise, and playing is the most natural way to get. The average student spends several hours a day in front of a TV or computer screen. Playing outside is much healthier. And studies show that active children get better grades, too.Believe it or not, play is important for adults too. More and more companies are realizing the value of playful work environment. Pixar, for example, encourages its employees to relax their minds and bodies through play. The company provides its workers with a game room, a pool and other fun areas. Pixar believes playful employees are more creative. Who knows? Maybe the idea for the animated film “cars” started out in the game room.88.When do babies begin learning the new world?________________________________________________________________89.Why is an empty box sometimes more fun than a high-tech toy?________________________________________________________________90.What do kid learn when they choose which toys to play with?________________________________________________________________91.Studies show that playful employees are more creative in companies, don’t they?________________________________________________________________92.What is a playful kid like?________________________________________________________________93.What suggestions will you give to those parents with kids?(give at least two sentences)________________________________________________________________94. Writing（作文）：（共20分）学校做了一次关于学生睡眠时间的调查，结果如下图。

上海民办新竹园中学小升初数学期末试卷测试卷（解析版）一、选择题1．我校每周一升旗仪式的时间是9：50，此时，分针与时针所夹的角是（）。

A．锐角B．直角C．钝角2．一种服装提价10%后是220元,求这种衣服的原价．正确的算式是()．A．220×(1+10%)B．220×(1-10%)C．220÷(1+10%)D．220÷(1-10%)3．一个三角形的三个内角的度数比是4∶5∶6，这个三角形是（）三角形。

A．锐角B．直角C．钝角4．某市出租车计费标准如表所示。

星期天，妈妈从家出发打车去商场，支付了18元，这段路程最长是几千米？设这段路程最长有x千米，下列方程正确的是（）。

3km以内（包括3km）3km以上（不足1km按1km计算）10元2元/kmA．10＋2x＝18 B．2（x－3）＝18 C．10＋2（x－3）＝18 D．10＋（x－3）＝185．一个由正方体组成的立体图形，从正面观察是，从左面观察是，从右面观察是，至少由（）个正方体组成的立体图形．A．3 B．5 C．6 D．76．如图，表示福福骑车从家到图书馆看书然后返回家的过程中离家的距离与时间的变化关系。

下面说法错误的是（）。

A．福福家到图书馆的距离是5千米B．福福去图书馆的骑车速度是10千米/小时C．福福在图书馆停留了2小时D．福福从图书馆返回家用了0.5小时7．图中，将长方形绕直线L旋转一周形成一个圆柱，这个圆柱的底面积是（）cm2。

A ．3.14B ．12.56C ．78.5 8．如果一种商品降价10％，再提价10％，那么，现在商品的价格与原来比较( )A ．相等B ．提高了C ．降低了 9．将一些小圆球如下图摆放，第六幅图有多少个小圆球？（ ）第一幅 第二幅 第三幅 第四幅A ．30B ．42C ．48D ．56二、填空题10．23时＝（______）分；4立方米30立方分米＝（______）立方米。

上海民办新竹园中学八年级下册期末物理试卷【解析】一、选择题1．下列表述中，符合生活实际的是（）A．托起两个鸡蛋所用的力约是1NB．洗澡水的温度约是85℃C．成人步行速度一般约是5m/sD．我们用的物理课本长约是5dm2．如图所示，骑自行车出行郊游，是一种时尚、环保的生活方式。

当我们在平直路面上匀速向前骑行时，以下说法正确的是（）A．人和车受到的重力与地面对人和车的支持力是相互作用力B．路面受到的压力与人受到的支持力是一对平衡力C．自行车受到的动力大于自行车受到的阻力D．自行车停下，惯性仍不会消失3．如图所示是“探究阻力对物体运动的影响”的实验，下列有关叙述正确的是（）A．三次实验小车从斜面静止下滑的位置可以不同B．运动的小车最终会停下来，说明物体的运动需要力来维持C．实验表明，小车受到的阻力越小，运动的距离越远D．根据二次实验现象进一步推理可以得出牛顿第一定律4．下列生活实例，属于增大压强的是（）A．刀剪用过一段时间要磨一磨B．推土机用宽大的履带来支撑C．铁轨下面铺放枕木D．书包的背带制作得较宽5．如图所示，烧杯和水的总质量是1kg，烧杯与水平桌面的接触面积是200cm2，将一个质量是700g、体积是1000cm3的立方体A用细线吊着，然后将其体积的一半浸入烧杯内的水中。

下列选项正确的是（）（烧杯厚度忽略不计，杯内水没有溢出，g=10N/kg，ρ水=1.0×103kg/m3）A．A受到的浮力为50NB．水对A底部的压强为50PaC．烧杯对水平桌面的压强是750PaD．若剪断绳子，待A静止后，水对容器底部增大的压力为5N6．如图所示，在杠杆OA上的B点悬挂一重物G，A端用细绳吊在小圆环E下，且细绳长AE等于圆弧半径，此时杠杆恰成水平状态，A点与圆环CED的圆心重合，当E环从C点逐渐顺时针滑到D点的过程中，吊绳对A端的拉力F大小与角θ的关系图像是（）A． B．C． D．7．物理兴趣小组的同学，做了一个浮沉子，如图所示．将装有适量水的玻璃小药瓶（如图甲）正好开口向下悬浮在封闭的大塑料瓶内的水中（如图乙），用力挤压大塑料瓶时，会发现玻璃小药瓶下沉（如图丙）．为了解释浮沉子下沉的现象，以下说法正确的是A．取玻璃小药瓶和小药瓶中的气体为研究对象,重力不变，浮力增大B．取玻璃小药瓶和小药瓶中的气体为研究对象,重力不变，浮力减小C．取玻璃小药瓶、小药瓶中气体和瓶中水为研究对象，重力不变，浮力减小D．取玻璃小药瓶、小药瓶中气体和瓶中水为研究对象，重力减小，浮力不变8．下图为起重机的钢丝绳吊着6×105N的重物匀速上升的图象，能正确反映钢丝绳的拉力所做的功与时间关系的是（）A．B．C． D．二、填空题9．用气球可以做很多物理小实验。

上海民办新竹园中学七年级下册数学期末试卷测试卷（解析版）一、解答题1．已知：如图（1）直线AB 、CD 被直线MN 所截，∠1＝∠2．（1）求证：AB //CD ；（2）如图（2），点E 在AB ，CD 之间的直线MN 上，P 、Q 分别在直线AB 、CD 上，连接PE 、EQ ，PF 平分∠BPE ，QF 平分∠EQD ，则∠PEQ 和∠PFQ 之间有什么数量关系，请直接写出你的结论；（3）如图（3），在（2）的条件下，过P 点作PH //EQ 交CD 于点H ，连接PQ ，若PQ 平分∠EPH ，∠QPF ：∠EQF ＝1：5，求∠PHQ 的度数．2．已知，如图1，射线PE 分别与直线AB ，CD 相交于E 、F 两点，∠PFD 的平分线与直线AB 相交于点M ，射线PM 交CD 于点N ，设∠PFM ＝α°，∠EMF ＝β°，且（40﹣2α）2＋|β﹣20|＝0（1）α＝ ，β＝ ；直线AB 与CD 的位置关系是 ；（2）如图2，若点G 、H 分别在射线MA 和线段MF 上，且∠MGH ＝∠PNF ，试找出∠FMN 与∠GHF 之间存在的数量关系，并证明你的结论；（3）若将图中的射线PM 绕着端点P 逆时针方向旋转（如图3），分别与AB 、CD 相交于点M 1和点N 1时，作∠PM 1B 的角平分线M 1Q 与射线FM 相交于点Q ，问在旋转的过程中1FPN Q∠∠的值是否改变？若不变，请求出其值；若变化，请说明理由． 3．综合与探究 （问题情境）王老师组织同学们开展了探究三角之间数量关系的数学活动（1）如图1，//EF MN ，点A 、B 分别为直线EF 、MN 上的一点，点P 为平行线间一点，请直接写出PAF ∠、PBN ∠和APB ∠之间的数量关系；（问题迁移）（2）如图2，射线OM 与射线ON 交于点O ，直线//m n ，直线m 分别交OM 、ON 于点A 、D ，直线n 分别交OM 、ON 于点B 、C ，点P 在射线OM 上运动，①当点P 在A 、B （不与A 、B 重合）两点之间运动时，设ADP α∠=∠，BCP β∠=∠．则CPD ∠，α∠，β∠之间有何数量关系？请说明理由．②若点P 不在线段AB 上运动时（点P 与点A 、B 、O 三点都不重合），请你画出满足条件的所有图形并直接写出CPD ∠，α∠，β∠之间的数量关系．4．如图，已知直线//AB 射线CD ，100CEB ∠=︒．P 是射线EB 上一动点，过点P 作PQ //EC 交射线CD 于点Q ，连接CP ．作PCF PCQ ∠=∠，交直线AB 于点F ，CG 平分ECF ∠．（1）若点P ，F ，G 都在点E 的右侧，求PCG ∠的度数；（2）若点P ，F ，G 都在点E 的右侧，30EGC ECG ∠-∠=︒，求CPQ ∠的度数； （3）在点P 的运动过程中，是否存在这样的情形，使:4:3EGC EFC ∠∠=？若存在，求出CPQ ∠的度数；若不存在，请说明理由．5．已知，如图：射线PE 分别与直线AB 、CD 相交于E 、F 两点，PFD ∠的角平分线与直线AB 相交于点M ，射线PM 交CD 于点N ，设PFM α∠=︒，EMF β∠=︒且()2350αβα-+-=．（1）α=________，β=________；直线AB 与CD 的位置关系是______；（2）如图，若点G 是射线MA 上任意一点，且MGH PNF ∠=∠，试找出FMN ∠与GHF ∠之间存在一个什么确定的数量关系？并证明你的结论．（3）若将图中的射线PM 绕着端点P 逆时针方向旋转（如图）分别与AB 、CD 相交于点1M 和点1N 时，作1PM B ∠的角平分线1M Q 与射线FM 相交于点Q ，问在旋转的过程中1FPN Q∠∠的值变不变？若不变，请求出其值；若变化，请说明理由．二、解答题6．如图，直线//PQ MN ，一副三角板（90ABC CDE ∠=∠=︒，30ACB ∠=︒，60,45EAC DCE DEC ∠=︒∠=∠=︒）按如图①放置，其中点E 在直线PQ 上，点,B C 均在直线MN 上，且CE 平分ACN ∠．（1）求DEQ ∠的度数．（2）如图②，若将三角形ABC 绕B 点以每秒5︒的速度按逆时针方向旋转（,A C 的对应点分别为,F G ）．设旋转时间为t 秒(036)t ≤≤． ①在旋转过程中，若边//BG CD ，求t 的值；②若在三角形ABC 绕B 点旋转的同时，三角形CDE 绕E 点以每秒4︒的速度按顺时针方向旋转（,C D 的对应点分别为,H K ）．请直接写出当边//BG HK 时t 的值．7．为更好地理清平行线相关角的关系，小明爸爸为他准备了四根细直木条AB 、BC 、CD 、DE ，做成折线ABCDE ，如图1，且在折点B 、C 、D 处均可自由转出．（1）如图2，小明将折线调节成50B ∠=︒，85C ∠=︒，35D ∠=︒，判断AB 是否平行于ED ，并说明理由；（2）如图3，若35C D ∠=∠=︒，调整线段AB 、BC 使得//AB CD 求出此时B 的度数，要求画出图形，并写出计算过程．（3）若85C ∠=︒，35D ∠=︒，//AB DE ，请直接写出此时B 的度数．8．已知：直线1l ∥2l ，A 为直线1l 上的一个定点，过点A 的直线交 2l 于点B ，点C 在线段BA 的延长线上．D ，E 为直线2l 上的两个动点，点D 在点E 的左侧，连接AD ，AE ，满足∠AED ＝∠DAE ．点M 在2l 上，且在点B 的左侧．（1）如图1，若∠BAD ＝25°，∠AED ＝50°，直接写出∠ABM 的度数 ；（2）射线AF 为∠CAD 的角平分线．① 如图2，当点D 在点B 右侧时，用等式表示∠EAF 与∠ABD 之间的数量关系，并证明； ② 当点D 与点B 不重合，且∠ABM ＋∠EAF ＝150°时，直接写出∠EAF 的度数 ．9．已知直线//AB CD ，M ，N 分别为直线AB ，CD 上的两点且70MND ∠=︒，P 为直线CD 上的一个动点．类似于平面镜成像，点N 关于镜面MP 所成的镜像为点Q ，此时,,NMP QMP NPM QPM MNP MQP ∠=∠∠=∠∠=∠．（1）当点P 在N 右侧时：①若镜像Q 点刚好落在直线AB 上（如图1），判断直线MN 与直线PQ 的位置关系，并说明理由；②若镜像Q 点落在直线AB 与CD 之间（如图2），直接写出BMQ ∠与DPQ ∠之间的数量关系；（2）若镜像PQ CD ⊥，求BMQ ∠的度数．10．如图，已知//AB CD P ，是直线AB CD ，间的一点，PF CD ⊥于点F PE ，交AB 于点120E FPE ∠=︒，．（1）求AEP ∠的度数；（2）如图2，射线PN 从PF 出发，以每秒40︒的速度绕P 点按逆时针方向旋转，当PN 垂直AB 时，立刻按原速返回至PF 后停止运动：射线EM 从EA 出发，以每秒15︒的速度绕E 点按逆时针方向旋转至EB 后停止运动，若射线PN ，射线EM 同时开始运动，设运动间为t 秒．①当20MEP ∠=︒时，求EPN ∠的度数； ②当 //EM PN 时，求t 的值．三、解答题11．如图，直线//AB CD ，E 、F 是AB 、CD 上的两点，直线l 与AB 、CD 分别交于点G 、H ，点P 是直线l 上的一个动点（不与点G 、H 重合），连接PE 、PF ．（1）当点P 与点E 、F 在一直线上时，GEP EGP ∠=∠，60FHP ∠=︒，则PFD ∠=_____．（2）若点P 与点E 、F 不在一直线上，试探索AEP ∠、EPF ∠、CFP ∠之间的关系，并证明你的结论．12．Rt △ABC 中，∠C=90°，点D 、E 分别是△ABC 边AC 、BC 上的点，点P 是一动点.令∠PDA=∠1，∠PEB=∠2，∠DPE=∠α.（1）若点P 在线段AB 上，如图（1）所示，且∠α=50°，则∠1+∠2= °；（2）若点P 在边AB 上运动，如图（2）所示，则∠α、∠1、∠2之间的关系为： ；（3）若点P 运动到边AB 的延长线上，如图（3）所示，则∠α、∠1、∠2之间有何关系？猜想并说明理由.（4）若点P 运动到△ABC 形外，如图（4）所示，则∠α、∠1、∠2之间的关系为： .13．【问题探究】如图1，DF ∥CE ，∠PCE=∠α，∠PDF=∠β，猜想∠DPC 与α、β之间有何数量关系？并说明理由； 【问题迁移】如图2，DF ∥CE ，点P 在三角板AB 边上滑动，∠PCE=∠α，∠PDF=∠β. （1）当点P 在E 、F 两点之间运动时，如果α=30°，β=40°，则∠DPC= °.（2）如果点P 在E 、F 两点外侧运动时（点P 与点A 、B 、E 、F 四点不重合），写出∠DPC 与α、β之间的数量关系，并说明理由．（图1） （图2）14．如图1，已知AB ∥CD ，BE 平分∠ABD ，DE 平分∠BDC ． （1）求证：∠BED ＝90°；（2）如图2，延长BE 交CD 于点H ，点F 为线段EH 上一动点，∠EDF ＝α，∠ABF 的角平分线与∠CDF 的角平分线DG 交于点G ，试用含α的式子表示∠BGD 的大小； （3）如图3，延长BE 交CD 于点H ，点F 为线段EH 上一动点，∠EBM 的角平分线与∠FDN 的角平分线交于点G ，探究∠BGD 与∠BFD 之间的数量关系，请直接写出结论： ．15．如图，//MN GH ，点A 、B 分别在直线MN 、GH 上，点O 在直线MN 、GH 之间，若116NAO ∠=︒，144OBH ∠=︒．（1）AOB ∠= ︒；（2）如图2，点C 、D 是NAO ∠、GBO ∠角平分线上的两点，且35CDB ∠=︒，求ACD ∠ 的度数；（3）如图3，点F 是平面上的一点，连结FA 、FB ，E 是射线FA 上的一点，若MAE ∠=n OAE ∠，HBF n OBF ∠=∠，且60AFB ∠=︒，求n 的值．【参考答案】一、解答题1．（1）见解析；（2）∠PEQ+2∠PFQ ＝360°；（3）30° 【分析】（1）首先证明∠1＝∠3，易证得AB//CD ；（2）如图2中，∠PEQ+2∠PFQ ＝360°．作EH//AB ．理由平行线 解析：（1）见解析；（2）∠PEQ +2∠PFQ ＝360°；（3）30° 【分析】（1）首先证明∠1＝∠3，易证得AB //CD ；（2）如图2中，∠PEQ +2∠PFQ ＝360°．作EH //AB ．理由平行线的性质即可证明； （3）如图3中，设∠QPF ＝y ，∠PHQ ＝x ．∠EPQ ＝z ，则∠EQF ＝∠FQH ＝5y ，想办法构建方程即可解决问题； 【详解】 （1）如图1中，∵∠2＝∠3，∠1＝∠2， ∴∠1＝∠3， ∴AB //CD ．（2）结论：如图2中，∠PEQ +2∠PFQ ＝360°． 理由：作EH //AB ．∵AB//CD，EH//AB，∴EH//CD，∴∠1＝∠2，∠3＝∠4，∴∠2+∠3＝∠1+∠4，∴∠PEQ＝∠1+∠4，同法可证：∠PFQ＝∠BPF+∠FQD，∵∠BPE＝2∠BPF，∠EQD＝2∠FQD，∠1+∠BPE＝180°，∠4+∠EQD＝180°，∴∠1+∠4+∠EQD+∠BPE＝2×180°，即∠PEQ+2(∠FQD+∠BPF)=360°，∴∠PEQ+2∠PFQ＝360°．（3）如图3中，设∠QPF＝y，∠PHQ＝x．∠EPQ＝z，则∠EQF＝∠FQH＝5y，∵EQ//PH，∴∠EQC＝∠PHQ＝x，∴x+10y＝180°，∵AB//CD，∴∠BPH＝∠PHQ＝x，∵PF平分∠BPE，∴∠EPQ+∠FPQ＝∠FPH+∠BPH，∴∠FPH＝y+z﹣x，∵PQ平分∠EPH，∴Z＝y+y+z﹣x，∴x＝2y，∴12y＝180°，∴y＝15°，∴x＝30°，∴∠PHQ＝30°．【点睛】本题考查了平行线的判定与性质，角平分线的定义等知识．（2）中能正确作出辅助线是解题的关键；（3）中能熟练掌握相关性质，找到角度之间的关系是解题的关键．2．（1）20，20，；（2）；（3）的值不变， 【分析】（1）根据，即可计算和的值，再根据内错角相等可证；（2）先根据内错角相等证，再根据同旁内角互补和等量代换得出； （3）作的平分线交的延长线于解析：（1）20，20，//AB CD ；（2）180FMN GHF ∠+∠=︒；（3）1FPN Q∠∠的值不变，12FPN Q=∠∠ 【分析】（1）根据2(402)|20|0αβ-+-=，即可计算α和β的值，再根据内错角相等可证//AB CD ； （2）先根据内错角相等证//GH PN ，再根据同旁内角互补和等量代换得出180FMN GHF ∠+∠=︒；（3）作1PEM ∠的平分线交1M Q 的延长线于R ，先根据同位角相等证//ER FQ ，得1FQM R =∠∠，设PER REB x ==∠∠，11PM R RM B y ==∠∠，得出12EPM R ∠=∠，即可得12FPN Q=∠∠． 【详解】解：（1）2(402)|20|0αβ-+-=，4020α∴-=，200β-=，20αβ∴==，20PFM MFN ∴∠=∠=︒，20EMF ∠=︒， EMF MFN ∴∠=∠，//AB CD ∴；故答案为：20、20，//AB CD ； （2）180FMN GHF ∠+∠=︒； 理由：由（1）得//AB CD ，MNF PME ∴∠=∠， MGH MNF ∠=∠， PME MGH ∴∠=∠，//GH PN ∴， GHM FMN ∴∠=∠， 180GHF GHM ∠+∠=︒，180FMN GHF ∴∠+∠=︒；（3）1FPN Q ∠∠的值不变，12FPN Q=∠∠；理由：如图3中，作1PEM ∠的平分线交1M Q 的延长线于R ，//AB CD ，1PEM PFN ∴∠=∠，112PER PEM ∠=∠，12PFQ PFN =∠∠，PER PFQ ∴∠=∠， //ER FQ ∴，1FQM R ∴∠=∠，设PER REB x ==∠∠，11PM R RM B y ==∠∠，则有：122y x Ry x EPM =+∠⎧⎨=+∠⎩，可得12EPM R ∠=∠，112EPM FQM ∴∠=∠，∴112EPM FQM ∠=∠． 【点睛】本题主要考查平行线的判定与性质，熟练掌握内错角相等证平行，平行线同旁内角互补等知识是解题的关键．3．（1）；（2）①，理由见解析；②图见解析，或 【分析】（1）作PQ ∥EF ，由平行线的性质，即可得到答案；（2）①过作交于，由平行线的性质，得到，，即可得到答案； ②根据题意，可对点P 进行分类讨论解析：（1）360PAF PBN APB ∠+∠+∠=°；（2）①CPD αβ∠=∠+∠，理由见解析；②图见解析，CPD βα∠=∠-∠或CPD αβ∠=∠-∠ 【分析】（1）作PQ ∥EF ，由平行线的性质，即可得到答案；（2）①过P 作//PE AD 交CD 于E ，由平行线的性质，得到DPE α∠=∠，CPE β∠=∠，即可得到答案；②根据题意，可对点P 进行分类讨论：当点P 在BA 延长线时；当P 在BO 之间时；与①同理，利用平行线的性质，即可求出答案．【详解】解：（1）作PQ ∥EF ，如图：∵//EF MN ，∴////EF MN PQ ，∴180PAF APQ ∠+∠=°，180PBN BPQ ∠+∠=°，∵APB APQ BPQ ∠=∠+∠∴360PAF PBN APB ∠+∠+∠=°；（2）①CPD αβ∠=∠+∠；理由如下：如图，过P 作//PE AD 交CD 于E ，∵//AD BC ，∴////AD PE BC ，∴DPE α∠=∠，CPE β∠=∠，∴CPD DPE CPE αβ∠=∠+∠=∠+∠；②当点P 在BA 延长线时，如备用图1：∵PE ∥AD ∥BC ，∴∠EPC=β，∠EPD =α，∴CPD βα∠=∠-∠；当P 在BO 之间时，如备用图2：∵PE∥AD∥BC，∴∠EPD=α，∠CPE=β，∴CPDαβ∠=∠-∠．【点睛】本题考查了平行线的性质，解题的关键是熟练掌握两直线平行同旁内角互补，两直线平行内错角相等，从而得到角的关系．4．（1）40°；（2）65°；（3）存在，56°或20°【分析】（1）依据平行线的性质以及角平分线的定义，即可得到∠PCG的度数；（2）依据平行线的性质以及角平分线的定义，即可得到∠ECG=∠G解析：（1）40°；（2）65°；（3）存在，56°或20°【分析】（1）依据平行线的性质以及角平分线的定义，即可得到∠PCG的度数；（2）依据平行线的性质以及角平分线的定义，即可得到∠ECG=∠GCF=25°，再根据PQ∥CE，即可得出∠CPQ=∠ECP=65°；（3）设∠EGC=4x，∠EFC=3x，则∠GCF=4x-3x=x，分两种情况讨论：①当点G、F在点E 的右侧时，②当点G、F在点E的左侧时，依据等量关系列方程求解即可．【详解】解：（1）∵∠CEB=100°，AB∥CD，∴∠ECQ=80°，∵∠PCF=∠PCQ，CG平分∠ECF，∴∠PCG＝∠PCF+∠FCG＝12∠QCF+12∠FCE=12∠ECQ=40°；（2）∵AB∥CD∴∠QCG=∠EGC，∠QCG+∠ECG=∠ECQ=80°，∴∠EGC+∠ECG=80°，又∵∠EGC-∠ECG=30°，∴∠EGC=55°，∠ECG=25°，∴∠ECG=∠GCF=25°，∠PCF=∠PCQ=12（80°-50°）=15°，∵PQ∥CE，∴∠CPQ=∠ECP=65°；（3）设∠EGC=4x，∠EFC=3x，则∠GCF=∠FCD=4x-3x=x，①当点G、F在点E的右侧时，则∠ECG=x，∠PCF=∠PCD=32 x，∵∠ECD=80°，∴x+x+32x+32x=80°，解得x=16°，∴∠CPQ=∠ECP=x+x+32x=56°；②当点G、F在点E的左侧时，则∠ECG=∠GCF=x，∵∠CGF=180°-4x，∠GCQ=80°+x，∴180°-4x=80°+x，解得x=20°，∴∠FCQ=∠ECF+∠ECQ=40°+80°=120°，∴∠PCQ＝12∠FCQ＝60°，∴∠CPQ=∠ECP=80°-60°=20°．【点睛】本题主要考查了平行线的性质，解题时注意：两直线平行，同旁内角互补；两直线平行，内错角相等．5．（1）35，35，平行；（2）∠FMN+∠GHF=180°，证明见解析；（3）不变，2【分析】（1）根据（α-35）2+|β-α|=0，即可计算α和β的值，再根据内错角相等可证AB∥CD；（2解析：（1）35，35，平行；（2）∠FMN +∠GHF =180°，证明见解析；（3）不变，2【分析】（1）根据（α-35）2+|β-α|=0，即可计算α和β的值，再根据内错角相等可证AB ∥CD ； （2）先根据内错角相等证GH ∥PN ，再根据同旁内角互补和等量代换得出∠FMN +∠GHF =180°；（3）作∠PEM 1的平分线交M 1Q 的延长线于R ，先根据同位角相等证ER ∥FQ ，得∠FQM 1=∠R ，设∠PER =∠REB =x ，∠PM 1R =∠RM 1B =y ，得出∠EPM 1=2∠R ，即可得1FPN Q∠∠=2． 【详解】解：（1）∵（α-35）2+|β-α|=0，∴α=β=35，∴∠PFM =∠MFN =35°，∠EMF =35°，∴∠EMF =∠MFN ，∴AB ∥CD ；（2）∠FMN +∠GHF =180°；理由：由（1）得AB ∥CD ，∴∠MNF =∠PME ，∵∠MGH =∠MNF ，∴∠PME =∠MGH ，∴GH ∥PN ，∴∠GHM =∠FMN ，∵∠GHF +∠GHM =180°，∴∠FMN +∠GHF =180°；（3）1FPN Q∠∠的值不变，为2， 理由：如图3中，作∠PEM 1的平分线交M 1Q 的延长线于R ，∵AB ∥CD ，∴∠PEM 1=∠PFN ，∵∠PER =12∠PEM 1，∠PFQ =12∠PFN ，∴∠PER =∠PFQ ，∴ER ∥FQ ，∴∠FQM 1=∠R ，设∠PER =∠REB =x ，∠PM 1R =∠RM 1B =y ，则有：122y x Ry x EPM ⎧⎨⎩=+∠=+∠， 可得∠EPM 1=2∠R ，∴∠EPM 1=2∠FQM 1， ∴11EPM FQM ∠∠=1FPN Q∠∠=2． 【点睛】本题主要考查平行线的判定与性质，熟练掌握内错角相等证平行，平行线同旁内角互补等知识是解题的关键．二、解答题6．（1）60°；（2）①6s ；②s 或s【分析】（1）利用平行线的性质角平分线的定义即可解决问题．（2）①首先证明∠GBC=∠DCN=30°，由此构建方程即可解决问题． ②分两种情形：如图③中，当解析：（1）60°；（2）①6s ；②103s 或703s 【分析】（1）利用平行线的性质角平分线的定义即可解决问题．（2）①首先证明∠GBC =∠DCN =30°，由此构建方程即可解决问题．②分两种情形：如图③中，当BG ∥HK 时，延长KH 交MN 于R ．根据∠GBN =∠KRN 构建方程即可解决问题．如图③-1中，当BG ∥HK 时，延长HK 交MN 于R ．根据∠GBN +∠KRM =180°构建方程即可解决问题．【详解】解：（1）如图①中，∵∠ACB=30°，∴∠ACN=180°-∠ACB=150°，∵CE平分∠ACN，∠ACN=75°，∴∠ECN=12∵PQ∥MN，∴∠QEC+∠ECN=180°，∴∠QEC=180°-75°=105°，∴∠DEQ=∠QEC-∠CED=105°-45°=60°．（2）①如图②中，∵BG∥CD，∴∠GBC=∠DCN，∵∠DCN=∠ECN-∠ECD=75°-45°=30°，∴∠GBC=30°，∴5t=30，∴t=6s．∴在旋转过程中，若边BG∥CD，t的值为6s．②如图③中，当BG∥HK时，延长KH交MN于R．∵BG∥KR，∴∠GBN=∠KRN，∵∠QEK=60°+4t，∠K=∠QEK+∠KRN，∴∠KRN=90°-（60°+4t）=30°-4t，∴5t=30°-4t，∴t=103s．如图③-1中，当BG∥HK时，延长HK交MN于R．∵BG∥KR，∴∠GBN+∠KRM=180°，∵∠QEK=60°+4t，∠EKR=∠PEK+∠KRM，∴∠KRM=90°-（180°-60°-4t）=4t-30°，∴5t+4t-30°=180°，∴t=703s．综上所述，满足条件的t的值为103s或703s．【点睛】本题考查几何变换综合题，考查了平行线的性质，旋转变换，角平分线的定义等知识，解题的关键是理解题意，学会用分类讨论的思想思考问题，学会利用参数构建方程解决问题，属于中考压轴题．7．（1）平行，理由见解析；（2）35°或145°，画图、过程见解析；（3）50°或130°或60°或120°【分析】（1）过点C作CF∥AB，根据∠B=50°，∠C=85°，∠D=35°，即可得C解析：（1）平行，理由见解析；（2）35°或145°，画图、过程见解析；（3）50°或130°或60°或120°【分析】（1）过点C作CF∥AB，根据∠B=50°，∠C=85°，∠D=35°，即可得CF∥ED，进而可以判断AB平行于ED；（2）根据题意作AB∥CD，即可∠B=∠C=35°；（3）分别画图，根据平行线的性质计算出∠B的度数．【详解】解：（1）AB平行于ED，理由如下：如图2，过点C作CF∥AB，∴∠BCF=∠B=50°，∵∠BCD=85°，∴∠FCD=85°-50°=35°，∵∠D=35°，∴∠FCD=∠D，∴CF∥ED，∵CF∥AB，∴AB∥ED；（2）如图，即为所求作的图形．∵AB∥CD，∴∠ABC=∠C=35°，∴∠B的度数为：35°；∵A′B∥CD，∴∠ABC+∠C=180°，∴∠B的度数为：145°；∴∠B的度数为：35°或145°；（3）如图2，过点C作CF∥AB，∵AB∥DE，∴CF∥DE，∴∠FCD=∠D=35°，∵∠BCD=85°，∴∠BCF=85°-35°=50°，∴∠B=∠BCF=50°．答：∠B的度数为50°．如图5，过C作CF∥AB，则AB∥CF∥CD，∴∠FCD=∠D=35°，∵∠BCD=85°，∴∠BCF=85°-35°=50°，∵AB∥CF，∴∠B+∠BCF=180°，∴∠B=130°；如图6，∵∠C=85°，∠D=35°，∴∠CFD =180°-85°-35°=60°，∵AB ∥DE ，∴∠B =∠CFD =60°，如图7，同理得：∠B =35°+85°=120°，综上所述，∠B 的度数为50°或130°或60°或120°．【点睛】本题考查了平行线的判定与性质，解决本题的关键是区分平行线的判定与性质，并熟练运用．8．（1）；（2）①，见解析；②或【分析】（1）由平行线的性质可得到：，，再利用角的等量代换换算即可；（2）①设，，利用角平分线的定义和角的等量代换表示出对比即可；②分类讨论点在的左右两侧的情况，解析：（1）125︒；（2）①2ABD EAF ∠=∠，见解析；②30或110︒【分析】（1）由平行线的性质可得到：DEA EAN =∠∠，MBA BAN =∠∠，再利用角的等量代换换算即可；（2）①设EAF α∠=，AED=DAE=β∠∠，利用角平分线的定义和角的等量代换表示出ABD ∠对比即可；②分类讨论点D 在B 的左右两侧的情况，运用角的等量代换换算即可．【详解】．解：（1）设在1l 上有一点N 在点A 的右侧，如图所示：∵12//l l∴DEA EAN =∠∠，MBA BAN =∠∠∴50AED DAE EAN ==︒∠＝∠∠∴255050125BAN BAD DAE EAN =++=︒+︒+︒=︒∠∠∠∠125BAM =︒∠（2）①2ABD=EAF ∠∠．证明：设EAF α∠=，AED=DAE=β∠∠．∴+=+FAD EAF DAE αβ=∠∠∠．∵AF 为CAD ∠的角平分线，∴22+2CAD FAD αβ==∠∠．∵12l l ，∴EAN=AED=β∠∠．∴2+22CAN CAD DAE EAN αβββα=--=--=∠∠∠∠．∴=22ABD CAN EAF α∠∠==∠．②当点D 在点B 右侧时，如图：由①得：2ABD EAF ∠=∠又∵180ABD ABM +=︒∠∠∴2180ABM EAF +=︒∠∠∵150ABM EAF ∠+∠︒＝∴18015030EAF =︒-︒=︒∠当点D 在点B 左侧，E 在B 右侧时，如图：∵AF 为CAD ∠的角平分线 ∴12DAF CAD =∠∠ ∵12l l∴AED NAE =∠∠，CAN ABE =∠∠∵DAE AED NAE ==∠∠∠∴11()22DAE DAE NAE DAN =+=∠∠∠∠ ∴11()(360)22EAF DAF DAE CAD DAN CAN =+=+=︒-∠∠∠∠∠∠ 11802ABE =︒-∠ ∵180ABE ABM +=︒∠∠∴11180(180)9022EAF ABM ABM =︒-︒-=︒+∠∠∠ 又∵150EAF ABM +=︒∠∠∴1190(150)16522EAF EAF EAF =︒+⨯︒-=︒-∠∠∠ ∴110EAF =︒∠当点D 和F 在点B 左侧时，设在2l 上有一点G 在点B 的右侧如图：此时仍有12DAE DAN =∠∠，12DAF CAD =∠∠∴11(360)1802211180(180)9022EAF DAE DAF CAN ABG ABM ABM =+=︒-=︒-=︒-︒-=︒+∠∠∠∠∠∠∠ ∴110EAF =︒∠综合所述：30EAF ∠=︒或110︒【点睛】本题主要考查了平行线的性质，角平分线的定义，角的等量代换等，灵活运用平行线的性质和角平分线定义等量代换出角的关系是解题的关键．9．（1）①，证明见解析，②，（2）或．【分析】(1) ①根据和镜像证出，即可判断直线与直线的位置关系，②过点Q 作QF ∥CD ，根据平行线的性质证即可；(2)过点Q 作QF ∥CD ，根据点P 的位置不同，解析：（1）①//MN PQ ，证明见解析，②70DPQ BMQ ∠∠+=︒，（2）160︒或20︒．【分析】(1) ①根据//AB CD 和镜像证出NMP QPM ∠=∠，即可判断直线MN 与直线PQ 的位置关系，②过点Q 作QF ∥CD ，根据平行线的性质证DPQ BM MQP Q ∠=∠∠+即可；(2)过点Q 作QF ∥CD ，根据点P 的位置不同，分类讨论，依据平行线的性质求解即可．【详解】（1）①//MN PQ ，证明：∵//AB CD ，∴NPM QMP ∠=∠，∵,NMP QMP NPM QPM ∠=∠∠=∠，∴NMP QPM ∠=∠，∴//MN PQ ；②过点Q 作QF ∥CD ，∵//AB CD ，∴////AB CD QF ，∴1BMQ ∠=∠，2QPD ∠=∠，∴DPQ BM MQP Q ∠=∠∠+，∵70MNP MQP ∠=∠=︒，∴70DPQ BMQ ∠∠+=︒；（2）如图，当点P 在N 右侧时，过点Q 作QF ∥CD ，同（1）得，////AB CD QF ，∴180NP FQP Q ∠=∠+︒，FQM BMQ ∠=∠，∵PQ CD ⊥，∴90NPQ ∠=︒，∴90FQP ∠=︒，∵70MND PQM ∠=∠=︒，∴20FQM ∠=︒，∴20BMQ ∠=︒，如图，当点P 在N 左侧时，过点Q 作QF ∥CD ，同（1）得，////AB CD QF ， 同理可得，90FQP ∠=︒，∵70MND ∠=︒，∴110MNP PQM ∠=∠=︒，∴20FQM ∠=︒，∵//AB QF ，∴180BM FQM Q ∠=∠+︒，∴160BMQ ∠=︒；综上，BMQ ∠的度数为160︒或20︒．【点睛】本题考查了平行线的性质与判定，解题关键是恰当的作辅助线，熟练利用平行线的性质推导角之间的关系．10．（1）；（2）①或；②秒或或秒【分析】（1）通过延长作辅助线，根据平行线的性质，得到，再根据外角的性质可计算得到结果；（2）①当时，分两种情况，Ⅰ当在和之间，Ⅱ当在和之间，由，计算出的运动时间解析：（1）30；（2）①2803︒或403︒；②185秒或5411或9011秒 【分析】（1）通过延长PG 作辅助线，根据平行线的性质，得到90∠=︒PGE ，再根据外角的性质可计算得到结果；（2）①当20MEP ∠=︒时，分两种情况，Ⅰ当ME 在AE 和EP 之间，Ⅱ当ME 在EP 和EB 之间，由20MEP ∠=︒，计算出EM 的运动时间t ，根据运动时间可计算出FPN ∠，由已知120FPE ∠=︒可计算出EPN ∠的度数； ②根据题意可知，当//EM PN 时，分三种情况，Ⅰ射线PN 由PF 逆时针转动，//EM PN ，根据题意可知15AEM t ∠=︒，40FPN t ∠=︒，再平行线的性质可得AEM AHP ∠=∠，再根据三角形外角和定理可列等量关系，求解即可得出结论；Ⅱ射线PN 垂直AB 时，再顺时针向PF 运动时，//EM PN ，根据题意可知，15AEM t ∠=︒，//ME PN ，15GHP t ∠=︒，可计算射线PN 的转动度数1809015t ︒+︒-︒，再根据PN 转动可列等量关系，即可求出答案；Ⅲ射线PN 垂直AB 时，再顺时针向PF 运动时，//EM PN ，根据题意可知，15AEM t ∠=︒，940()2GPN t ∠=-︒，根据（1）中结论，30PEG ∠=︒，60PGE ∠=，可计算出PEM ∠与EPN ∠代数式，再根据平行线的性质，可列等量关系，求解可得出结论．【详解】解：（1）延长FP 与AB 相交于点G ，如图1，PF CD ⊥，90PFD PGE ∴∠=∠=︒，EPF PGE AEP ∠=∠+∠，1209030AEP EPF PGE ∴∠=∠-∠=︒-︒=︒；（2）①Ⅰ如图2，30AEP ∠=︒，20MEP ∠=︒，10AEM ∴∠=︒，∴射线ME 运动的时间102153t ==（秒)， ∴射线PN 旋转的角度2804033FPN ︒∠=⨯︒=， 又120EPF ∠=︒，8028012033EPN EPF EPN ︒︒∴∠=∠-∠=︒-=；Ⅱ如图3所示，30AEP ∠=︒，20MEP ∠=︒，50AEM ∴∠=︒，∴射线ME 运动的时间5010153t ==（秒)， ∴射线PN 旋转的角度104004033FPN ︒∠=⨯︒=， 又120EPF ∠=︒，4004012033EPN FPN EPF ︒︒∴∠=∠-∠=-︒=； EPN ∴∠的度数为2803︒或403︒；②Ⅰ当PN 由PF 运动如图4时//EM PN ，PN 与AB 相交于点H ，根据题意可知，经过t 秒，15AEM t ∠=︒，40FPN t ∠=︒，//EM PN ，15AEM AHP t ∴∠=∠=︒，又=FPN PGH PHA ∠∠+∠，409015t t ∴︒=︒+︒， 解得185t =（秒)；Ⅱ当PN 运动到PG ，再由PG 运动到如图5时//EM PN ，PN 与AB 相交于点H ，根据题意可知，经过t 秒，15AEM t ∠=︒，//EM PN ，15GHP t ∴∠=︒，9015GPH t ∠=︒-︒，PN ∴运动的度数可得，18040GPH t ︒+∠=︒，解得5411t =；Ⅲ当PN 由PG 运动如图6时，//EM PN ，根据题意可知，经过t 秒，15AEM t ∠=︒，40180GPN t ∠=-︒，30AEP ∠=︒，60EPG ∠=︒，1530PEM t ∴∠=︒-︒，24040EPN t ∠=︒-，又//EM PN ，180PEM EPN ∴∠+∠=︒，153040240180t t ∴︒-︒+-︒=︒， 解得9011t =（秒）， 当t 的值为185秒或5411或9011秒时，//EM PN ．【点睛】本题主要考查平行线性质，合理添加辅助线和根据题意画出相应的图形时解决本题的关键．三、解答题11．（1）120°；（2）∠EPF =∠AEP+∠CFP 或∠AEP=∠EPF+∠CFP ，证明见详解．【分析】（1）根据题意，当点与点、在一直线上时，作出图形，由AB ∥CD ，∠FHP=60°，可以推出解析：（1）120°；（2）∠EPF =∠AEP+∠CFP 或∠AEP=∠EPF+∠CFP ，证明见详解．【分析】（1）根据题意，当点P 与点E 、F 在一直线上时，作出图形，由AB ∥CD ，∠FHP=60°，可以推出GEP EGP ∠=∠=60°，计算∠PFD 即可；（2）根据点P 是动点，分三种情况讨论：①当点P 在AB 与CD 之间时；②当点P 在AB 上方时；③当点P 在CD 下方时，分别求出∠AEP 、∠EPF 、∠CFP 之间的关系即可．【详解】（1）当点P 与点E 、F 在一直线上时，作图如下，∵AB ∥CD ，∠FHP=60°，GEP EGP ∠=∠，∴GEP EGP ∠=∠=∠FHP=60°，∴∠EFD=180°-∠GEP=180°-60°=120°，∴∠PFD=120°，故答案为：120°；（2）满足关系式为∠EPF =∠AEP+∠CFP或∠AEP=∠EPF+∠CFP．证明：根据点P是动点，分三种情况讨论：①当点P在AB与CD之间时，过点P作PQ∥AB，如下图，∵AB∥CD，∴PQ∥AB∥CD，∴∠AEP=∠EPQ，∠CFP=∠FPQ，∴∠EPF=∠EPQ+∠FPQ=∠AEP+∠CFP，即∠EPF =∠AEP+∠CFP；②当点P在AB上方时，如下图所示，∵∠AEP=∠EPF+∠EQP，∵AB∥CD，∴∠CFP=∠EQP，∴∠AEP=∠EPF+∠CFP；③当点P在CD下方时，∵AB∥CD，∴∠AEP=∠EQF，∴∠EQF=∠EPF+∠CFP，∴∠AEP=∠EPF+∠CFP，综上所述，∠AEP、∠EPF、∠CFP之间满足的关系式为：∠EPF =∠AEP+∠CFP或∠AEP=∠EPF+∠CFP，故答案为：∠EPF =∠AEP+∠CFP或∠AEP=∠EPF+∠CFP．【点睛】本题考查了平行线的性质，外角的性质，掌握平行线的性质是解题的关键，注意分情况讨论问题．12．（1）140°；（2）∠1+∠2=90°+α；（3）∠1=90°+∠2+α,理由见解析;(4)∠2=90°+∠1﹣α．【详解】试题分析：（1）根据四边形内角和定理以及邻补角的定义，得出∠1+∠2解析：（1）140°；（2）∠1+∠2=90°+α；（3）∠1=90°+∠2+α,理由见解析;(4)∠2=90°+∠1﹣α．【详解】试题分析：（1）根据四边形内角和定理以及邻补角的定义，得出∠1+∠2=∠C+∠α，进而得出即可；（2）利用（1）中所求的结论得出∠α、∠1、∠2之间的关系即可；（3）利用三角外角的性质，得出∠1=∠C+∠2+α=90°+∠2+α；（4）利用三角形内角和定理以及邻补角的性质可得出∠α、∠1、∠2之间的关系．试题分析：（1）∵∠1＋∠2＋∠CDP＋∠CEP＝360°，∠C＋∠α＋∠CDP＋∠CEP＝360°，∴∠1＋∠2＝∠C＋∠α，∵∠C＝90°，∠α＝50°，∴∠1＋∠2＝140°，故答案为140；（2）由(1)得∠α＋∠C＝∠1＋∠2，∴∠1＋∠2＝90°＋∠α.故答案为∠1＋∠2＝90°＋∠α.（3）∠1＝90°＋∠2＋∠α.理由如下：如图③，设DP与BE的交点为M，∵∠2＋∠α＝∠DME，∠DME＋∠C＝∠1，∴∠1＝∠C＋∠2＋∠α＝90°＋∠2＋∠α.（4）如图④，设PE与AC的交点为F，∵∠PFD＝∠EFC，∴180°－∠PFD＝180°－∠EFC，∴∠α＋180°－∠1＝∠C＋180°－∠2，∴∠2＝90°＋∠1－∠α.故答案为∠2＝90°＋∠1－∠α点睛：本题考查了三角形内角和定理和外角的性质、对顶角相等的性质，熟练掌握三角形外角的性质是解决问题的关键.13．∠DPC=α+β，理由见解析；（1）70 ；(2) ∠DPC=α –β，理由见解析.【解析】（1）过P作PE∥AD交CD于E，推出AD∥PE∥BC，根据平行线的性质得出∠α=∠DPE，∠β=∠C解析：∠DPC=α+β，理由见解析；（1）70 ；(2) ∠DPC=α –β，理由见解析.【解析】（1）过P作PE∥AD交CD于E，推出AD∥PE∥BC，根据平行线的性质得出∠α=∠DPE，∠β=∠CPE，即可得出答案；（2）化成图形，根据平行线的性质得出∠α=∠DPE，∠β=∠CPE，即可得出答案．【问题探究】解：∠DPC=α+β如图，过P作PH∥DF∵DF∥CE,∴∠PCE=∠1=α，∠PDF=∠2∵∠DPC=∠2+∠1=α+β【问题迁移】（1）70（图1）（图2）(2) 如图1，∠DPC=β -α∵DF∥CE,∴∠PCE=∠1=β，∵∠DPC=∠1-∠FDP=∠1-α．∴∠DPC=β -α如图2，∠DPC= α -β∵DF∥CE,∴∠PDF=∠1=α∵∠DPC=∠1-∠ACE=∠1-β．∴∠DPC=α - β14．（1）见解析；（2）∠BGD＝；（3）2∠BGD+∠BFD＝360°．【分析】（1）根据角平分线的性质求出∠EBD+∠EDB＝（∠ABD+∠BDC），根据平行线的性质∠ABD+∠BDC＝180°解析：（1）见解析；（2）∠BGD＝902a︒-；（3）2∠BGD+∠BFD＝360°．【分析】（1）根据角平分线的性质求出∠EBD+∠EDB＝12（∠ABD+∠BDC），根据平行线的性质∠ABD+∠BDC＝180°，从而根据∠BED＝180°﹣（∠EBD+∠EDB）即可得到答案；（2）过点G作GP∥AB，根据AB∥CD，得到GP∥AB∥CD，从而得到∠BGD＝∠BGP+∠PGD＝∠ABG+∠CDG，然后根据∠EBD+∠EDB＝90°，∠ABD+∠BDC＝180°，得到∠ABE+∠EDC＝90°，即∠ABE+α+∠FDC＝90°，再利用角平分线的定义求出2∠ABG+2∠CDG＝90°﹣α即可得到答案；（3）过点F、G分别作FM∥AB、GM∥AB，从而得到AB∥GM∥FN∥CD，得到∠BGD＝∠BGM+∠DGM＝∠4+∠6，根据BG平分∠FBP，DG平分∠FDQ，∠4＝12∠FBP＝12（180°﹣∠3），∠6＝12∠FDQ＝12（180°﹣∠5），即可求解.【详解】解：（1）证明：∵BE平分∠ABD，∴∠EBD＝12∠ABD，∵DE平分∠BDC，∴∠EDB＝12∠BDC，∴∠EBD+∠EDB＝12（∠ABD+∠BDC），∵AB∥CD，∴∠ABD+∠BDC＝180°，∴∠EBD+∠EDB＝90°，∴∠BED＝180°﹣（∠EBD+∠EDB）＝90°．（2）解：如图2，由（1）知：∠EBD+∠EDB＝90°，又∵∠ABD+∠BDC＝180°，∴∠ABE+∠EDC＝90°，即∠ABE+α+∠FDC＝90°，∵BG平分∠ABE，DG平分∠CDF，∴∠ABE＝2∠ABG，∠CDF＝2∠CDG，∴2∠ABG+2∠CDG＝90°﹣α，过点G作GP∥AB，∵AB∥CD，∴GP∥AB∥CD∴∠ABG＝∠BGP，∠PGD＝∠CDG，∴∠BGD＝∠BGP+∠PGD＝∠ABG+∠CDG＝902α-；（3）如图，过点F、G分别作FN∥AB、GM∥AB，∵AB∥CD，∴AB∥GM∥FN∥CD，∴∠3＝∠BFN ，∠5＝∠DFN ，∠4＝∠BGM ，∠6＝∠DGM ，∴∠BFD ＝∠BFN +∠DFN ＝∠3+∠5，∠BGD ＝∠BGM +∠DGM ＝∠4+∠6，∵BG 平分∠FBP ，DG 平分∠FDQ ，∴∠4＝12∠FBP ＝12（180°﹣∠3），∠6＝12∠FDQ ＝12（180°﹣∠5），∴∠BFD +∠BGD ＝∠3+∠5+∠4+∠6，＝∠3+∠5+12（180°﹣∠3）+12（180°﹣∠5），＝180°+12（∠3+∠5），＝180°+12∠BFD ，整理得：2∠BGD +∠BFD ＝360°．【点睛】本题主要考查了平行线的性质与判定，角平分线的性质和三角形内角和定理，解题的关键在于能够熟练掌握相关知识进行求解.15．（1）100；（2）75°；（3）n=3．【分析】（1）如图：过O 作OP//MN ，由MN//OP//GH 得∠NAO+∠POA=180°，∠POB+∠OBH=180°，即∠NAO+∠AOB+∠OB解析：（1）100；（2）75°；（3）n =3．【分析】（1）如图：过O 作OP //MN ，由MN //OP //GH 得∠NAO +∠POA =180°，∠POB +∠OBH =180°，即∠NAO +∠AOB +∠OBH =360°，即可求出∠AOB ；（2）如图：分别延长AC 、CD 交GH 于点E 、F ，先根据角平分线求得58NAC ∠=︒，再根据平行线的性质得到58CEF ∠=︒；进一步求得18DBF ∠=︒，17DFB ∠=︒，然后根据三角形外角的性质解答即可；（3）设BF 交MN 于K ，由∠NAO =116°，得∠MAO =64°，故∠MAE =641n n ︒⨯+，同理∠OBH =144°，∠HBF =n ∠OBF ，得∠FBH =1441n n ︒⨯+，从而=n BKA FBH n ∠∠=⨯︒+1441，又∠FKN =∠F +∠FAK ，得144606411n n n n ︒︒︒⨯=+⨯++，即可求n ． 【详解】解：（1）如图：过O 作OP //MN ，∵MN //GHl∴MN //OP //GH ∴∠NAO +∠POA =180°，∠POB +∠OBH =180°∴∠NAO +∠AOB +∠OBH =360°∵∠NAO =116°，∠OBH =144°∴∠AOB =360°-116°-144°=100°；（2）分别延长AC 、CD 交GH 于点E 、F ，∵AC 平分NAO ∠且116NAO ∠=︒，∴58NAC ∠=︒，又∵MN //GH ，∴58CEF ∠=︒；∵144OBH ∠=︒，36OBG ∠=︒∵BD 平分OBG ∠，∴18DBF ∠=︒，又∵,CDB ∠=︒35∴351817DFB CDB DBF ∠=∠-∠=-=︒；∴175875ACD DFB AEF ∠=∠+∠=︒+︒=︒；（3）设FB 交MN 于K ，∵116NAO ∠=︒，则MAO ∠=︒64；∴641n MAE n ∠=⨯︒+ ∵144OBH ∠=︒， ∴+1n FBH n ∠=⨯︒144，=n BKA FBH n ∠∠=⨯︒+1441， 在△FAK 中，64601n BKA FKA F n ∠=∠+∠=⨯︒+︒+, ∴144646011n n n n ⨯︒=⨯︒+︒++， ∴3n =．经检验：3n =是原方程的根，且符合题意.【点睛】本题主要考查平行线的性质及应用，正确作出辅助线、构造平行线、再利用平行线性质进行求解是解答本题的关键．。

2017年上海民办新竹园中学9B考9Part 2 Phonetics Grammar and Vocabulary（第二部分语音、语法和词汇）II．Choose the best answer（选择最恰当的答案）：（共20分）26.Which of the following underlined parts is different in pronunciation from the others?A.His perception of the change came in a flash.B. The population gravitates towards the city.C.He had some motive in telling this fable.D. A good relationship is built on trust.27.The mother looked at his son with ________ on her face because he achieved his goal.A. joyfulB. joyC. worryD. worried28.Learning ________ country’s language is a better way of knowing ________ culture behind it.A. the, aB. a, theC. /, theD. a, /29.All of us went to the park ________ Bob. He had to look after his sister.A. besidesB. withC. exceptD. and30.- What is your mother going to do this Saturday?- I'm not sure. She ________ go to see my grandmother.A. canB. mayC. mustD. can’t31.- ________ will you stay in Shanghai?- For about three weeks.A. How soonB. How farC. How oftenD. How long32.She saw some boys ________ soccer on the playground when she was on the way to the classroom.A. playB. to playC. playingD. played33.________ is important and necessary for us ________ English well.A. This… to learn B．It… learning C. That... learning D. It... to learn34.She doesn't tell me when she ________ . I' l1 tell you as soon as she ________ .A. will come ... comesB. will come... will comeC. comes… will comeD. comes… comes35.Excuse me. Could you tell me ________ later on?A. if the next train arrivesB. when the next train arrivesC. if the next train will arriveD. when will the next train arrive36.About 6,000, 000 graduates in China are looking for jobs. Some companies are likely to leave more jobs open,________others are cutting jobs.A. soB. andC. butD. or37.The successful space walk of Zhai zhigang is helpful to ________ a space station.A. look upB. take upC. set upD. pick up38.When we got to the airport, we were told that they ________ more than 5000 people from the ruins by earthquake.A. has savedB. had savedC. savedD. have saved39.Taking a walk in the evening is a good ________ . So it is; it keeps us healthy.A. habitB. hobbyC. ruleD. favor40.What a beautiful factory! I hope I will work in it.Well, workers ________ very much here.A. needB. are needingC. are neededD. will need41.The teacher has already to ld me but I’m still not clear ________ to do next.A. howB. whatC. whyD. whether42.We must do everything we can ________ waste water from running into rivers.A. keepB. keptC. to keepD. keeping43.The weather forecast ________ it will be rainy in the late afternoon.A. tellsB. saysC. speaksD. talks44.About ________ of the computers in this room are online.A. two-fifthB. two-fifthsC. second-fivesD. second-fifths45.- Would you like to go for a picnic this weekend? Let’s enjoy the fresh air outside.- ________. It will be a sunny day.A. It's a pleasure.B. Don't mention it.C. No, I won't.D. I’d love to.III. Complete the following passage with the words or phrases in the box. Each word or phrase can only be usedNow lots of parents will buy everything that their children want to have. If they 46 the habit, their children won’t know the money come s from hard work.Some parents like to hold birthday parties for their children. If they keep on doing this, their children will think it 47 for them to enjoy birthday parties every year. Year after year, maybe they will forget their parents’ birthda ys and only remember their own. It is 48 traditional habits.Many parents don' t let the children do housework. They think children have only one thing to do. They should study hard and do well in their lessons. If parents go on doing this, the children will only learn to their mouths to be fed and stretch out their arms to 49 every day. When the children grow up, they will be able to do nothing, and they won't even find a job. Parents should teach the children how to do housework because it can help them start good habits of working by themselves.There once was a little boy who wanted to meet God. He knew it was a long trip, so he 50 his suitcase with cakes and a six-pack of beer, and started his journey.When he had gone about three blocks, he met an old woman. She was sitting in the park, staring at some pigeons. The boy sat down next to her and opened his suitcase. He was about to take a drink when he noticed that the old lady looked hungry, so he offered her a cake.She 51 accepted it and smiled at him. Her smile was so pretty that the boy wanted to see it again, so he offered her some beer.Once again, she smiled at him. The boy was delighted. They sat there all afternoon eating and smiling, yet they never said a word.As it grew dark, the boy got up to leave. Before he had gone more than a few steps, he 52 , ran back to the old woman and gave her a hug. She gave him her biggest smile ever.When the boy got home, his mother was surprised by the look of joy on his fa ce. She asked him, “What did you do today that made you so happy?” He replied, “I had lunch with God. But before his mother could respond, he added. “You now what? She’s got the most beautiful smile I’ve ever seen!”53 , the old woman returned to her home. Her neighbor was shocked by the look of joy on her face and asked, “What did you do today that made you so happy?”She replied, “I ate cakes in the Park with God.” But before her neighbor responded, she added, “You know he’s much younger than I expe cted.”IV. Complete the sentences with the given words in their proper forms（用括号中所给单词的适当形式完成下列句子，每空格限填一词）（共8分）54.To save money, using coupons becomes one of the most popular shopping ________ in America.(act)55.Some teenagers are used to reading ________ magazines online.(electricity)56.It is ________ for him to be late for class. Everyone knows he is a good student. (usual)57.Mom has bought a lot of ________ food from the supermarket nearby.(freeze)58.I haven’ t seen you for a long time. You look far ________(pretty).59.Not all the people who had received Peter’s invitations ________ the party (attend)60.You ________ helped me a lot. Thank you very much indeed.(real)61.The _______ month of the year is September when we all start our school. (nine)V. Rewrite the following sentences as required（根据所给要求改写下列句子。

上海民办新竹园中学物理八年级下册期末试卷【解析】一、选择题1．下列物理量的大小与实际相符的是（）A．一个鸡蛋重约为5NB．一个中学生双脚站立在水平地面上产生的压强约为1.6×106PaC．一标准大气压下你的拇指指甲盖受到大气压力约为1ND．将一本掉在地上的物理书捡起放到课桌上所做的功约为2J2．下列情况下，物体受平衡力作用的是（）A．苹果从树上落下来B．汽车在弯道上匀速转弯C．物体在水平路面上匀速直线前进D．向上抛出的石块3．图小车上表面水平足够长且无摩擦，上面放置的物块A、B与小车一起以相同速度v向右匀速直线运动，不计空气阻力。

小车遇到障碍物立刻停止，A、B会否在车上相撞？（）A．不会，与A、B质量无关B．可能会，与A、B质量有关C．可能会，与A、B初始间距有关D．一定会，与A、B初始间距无关4．如图所示的实例中，属于增大压强的是（）A．图钉帽做得很大B．喝饮料的管一端很尖C．铁轨下的枕木D．滑雪用的雪橇5．水平桌面上两个容器中分别盛有甲、乙两种液体。

将小球A先后放入两个容器中，静止时小球状态如图所示（两个容器液面相平）。

下列说法正确的是（）A．两种液体的密度ρ甲>ρ乙B．小球所受浮力F甲＜F乙C．小球所受浮力F甲>F乙D．两容器底受到液体压强p甲=p乙AO OB ，甲、乙两物体重均为6．如图所示，轻质杠杆AC可以绕O点转动，:3:1300N，甲的底面积为4cm2，杠杆始终保持水平平衡，下列说法正确的是（）A ．甲对地面的压强为5×105PaB ．地面对甲的支持力为100NC ．A 端受到甲的拉力为200ND ．物体乙从B 点向C 点移动过程中，甲对地面的压强逐渐增大7．如图所示，完全相同的甲、乙两个圆柱形容器盛有质量相等的水，放在水平桌面上．现 有体积均为400cm 2的长方体物块A 、B ，己知物块B 的密度为0.25×103kg/m 3，现用细线 将A 、B 两物块分别与天花板和容器底部相连，使其部分浸入水中，如图甲、乙所示， 此时物块A 、B 均有14体积露出水面，且细线的拉力均为F ，则下列判断错误的是A ．拉力F 的大小为2 NB ．物体A 的密度为1.25 g/cm 3C ．甲、乙容器中水对容器底的压强增加量相等D ．放入物体后，甲、乙两容器对桌面的压力相等8．在自由下落过程中物体运动速度会越来越快．一个物体由A 点自由下落，相继经过B 、C 两点，已知AB BC =，如图所示，物体在AB 段重力做功1W ，做功功率1P ；在BC 段重力做功2W ，做功功率P 2，则下列关系正确的是（ ）A ．12W W ≠；12P P ≠B ．12W W =；12P P =C ．12W W =；12>P PD ．12W W =；12<P P二、填空题9．如图所示，是在排球比赛中成功拦网的情景，主要说明了力可以改变物体的___________；当运动员拦下排球时，手感到疼痛，这表明物体间力的作用是___________的；用力按压排球时，排球会变扁，说明力可以改变物体的___________。

上海民办新竹园中学2017学年第二学期数学学科七年级阶段性诊断二试卷（满分：100分，时间：60分钟）一、填空题1、已知6=a ，102=b ，且a b b a -=-，则=+b a .【解析】略【答案】2或42、若b a ,为实数，且471122++-+-=a a ab ，则b a +的值为 . 【解析】略【答案】3或53、已知m 满足m m m =-+2011-1，则m = .【解析】略【答案】20124、一个等腰三角形的两条边长分别为32和25，则此等腰三角形的周长为 .【解析】略 【答案】21032+5、已知ADE ∆≌ABC ∆，AC AB =，且ABC ∆的周长为23厘米，4=BC 厘米，则DEF ∆的边中必有一边等于 .【解析】略 【答案】219厘米或4厘米 6、一个三角形的三条边为2、5、x ，另一个三角形的三边为Y 、2、6，若这两个三角形全等，则=+y x . 【解析】略【答案】117、在ABC ∆中，AC AB =，AB 的垂直平分线与边AC 所在的直线相交成锐角为︒50，ABC ∆的底脚B ∠的大小为 .【解析】略【答案】︒︒2070或8、在ABC ∆中，︒=∠60C ，6=BC ，4=AC ，AD 是高，将ACD ∆沿着AD 翻折，点C 落在点E 上，那么BE 的长是 .【解析】略【答案】29、如图，在ABC ∆中，AC AB =，若将ABC ∆绕点C 顺时针旋转得C B A ''∆，使点'B 落在线段AB 上，如果︒=∠75B ，则=∠'ACA 度.（第9题）【解析】略【答案】3010、如图，D 为BC 的中点，E 为AD 的中点，则ABE ∆的面积与ABC ∆的面积之比为 .【解析】略【答案】1:411、写出命题“直角三角形斜边上的中线等于斜边的一半”的逆命题：【解析】略【答案】在三角形中，一边上的中线等于这边的一半，则这个三角形为直角三角形12、若点N 到x 轴的距离为1，到y 轴的距离为2，则点N 的坐标为【解析】略【答案】（-2.-1）；（2，-1）；（2,1）；（-2,1）13、观察有序实数对：（3，-1）、（-5，21）、（7，31-）、（-9，41）······根据你发现的规律，第100个有序实数对点是【解析】寻找规律，观察后发现第n 个有序实数对可以表示为[)12(1-1+∙+n n ）（,nn 11-∙）（] 【答案】），（1001- 201- 二、选择题14、近似数1.30所表示的准确数A 的取值范围是（ ）【】35.125.1<≤A 【B 】30.120.1<<A【C 】305.125.1<≤A 【D 】305.1300.1<≤A【解析】略【答案】C15、已知：ABC ∆≌DEF ∆，︒=∠=∠90D A ，︒=∠37B ，则=∠E （ ）【】︒37 【B 】︒53 【C 】︒︒5337或 【D 】︒︒6337或【解析】略【答案】A A A16、如果0=xy ，则点）（y x P ,的位置点（ ） 【】在数轴上 【B 】在去掉原点的横轴上【C 】在纵轴上 【D 】在去掉原点的纵轴上【解析】略【答案】B17、下列命题：（1）有两个角和第三个角的平分线对应相等的两个三角形全等；（2）有两条边和第三条边上的中线对应相等的两个三角形全等；（3）有两条边和第三边上的高对应相等的两个三角形全等。

上海民办新竹园中学2017学年第二学期英语学科九年级考10试卷Part 1 Listening (第一部分听力)I.Listening Comprehension (听力理解)(共30分)A．Listen and choose the right picture（根据你听到的内容，选出相应的图片）：（6分）1.________2.________3.________4.________5.________6._______B.Listen to the dialogue and choose the best answer to the question you hear.(根据你听到的对话和问题，选出最恰当的答案) (8分)7.A)Jim. B)Jenny. C)Lily D.Linda8.A)A TV play B) The TV news C)Their past D)Their hometown.9. A)By asking for them from a friend. B)By lining up in front of the ticket officeC)By booking them on the phone D)By buying them from someone else10. A)He had lost Mr. Smith's dictionaryB)He had forgotten to bring Mr. Smith' s dictionary.C)He had forgotten to give Mr. Smith the dictionaryD)He had forgotten to tell Mr. Smith to bring the dictionary.11. A)In a bookshop. B)In a library. C)In a hospital D) In a store12. A)Eight hours B)Six hours C)Three hours D)One hour.13. A )After one o'clock. B)Before twelve o'clock.C)Before one o'clock. D)At a quarter past twelve.14. A)Mother and teacher B)Mother and sonC)Father and teacher D)Teacher and studentC.Listen to the passage and tell whether the following statements are true or false(判断下列句子是否符合你听到的短文内容，符合的用“T”表示，不符合的用“F"表示)（共6分）15.John Slack went to Royal Hotel to book a room.16.He needed a single room or the 15th of October room17.He wanted to enjoy the beautiful lake view in the room.18.He must pay $840 for his stay in the hotel with breakfast.19.He can check in at 12:30 pm when he arrives at the hotel. %.20.This dialogue is mainly about how to book a hotel roomD. Listen to the passage and complete the following sentences(听短文,完成下列内容,每空格限填一词):(共10分)21.Let me tell you stories of great animal parers.22.After the heavy rain, a dog swam to an island .23.The mother dog swam to the island every day to feed .24.Chimpanzees (a )also cared for those that got lost.25.The brave parents rushed down to the road and took the bird away.Part 2 Phonetics, Grammar and Vocabulary(第二部分语音、语法和词汇)I.Choose the best answer(选择最恰当的答案):(共20分)26.Which of the following underlined parts is different in pronunciation from the others?A)You will be able to read in peace B)Shall I ask for a large steak?C)Ice cream is high in fat and sugar. D)Who is weak in spelling in class?27.Spring Festival is wonderful time for people to visit friends and relax.A)a B)an C)the D)/28.The charity walkers arrived at the small town a rainy morning.A)in B)at C)on D)of29.This match provides us _________ an excellent chance to try out some new players.A)from B) about C)for D) with30.More than half a million British people have a second home in .A)other B)the other C)another D) others31.can learn how to surf the Internet safely and effectively in computer lessons in other country.A)You B)Your C)Yours D) Yourself32.Doing eye exercises is one of ways to protect your eyes.A)good B)better C)best D) the best33.He looked at the young man and couldn’t say a word.A)friendly B)angrily C)lonely D)lovely34.Would you like the sunshine on the beach with me?A)enjoy B)enjoying C)to enjoy D) enjoyed35.Peter keeps us he’s going to be a famous artist before he’s 40.A)tell B)telling C)to tell D)told36.you lend me your spare pen？I have left mine at home.A)May B)Should C)Must D)Could37.I your email after the meeting and see whether it’s there or not.A)will check B)am checking C)have checked D)checked38.Paul failed his driving test because he enough before.A)wasn’t practising B)doesn’t practise C)hadn’t practised. D)wouldn’t practise39.People to send up fireworks around the centre of the city last Spring FestiveA)weren't allowed B)won't be allowed C)are not allowed D)haven’t been allowed40.I like reading, I always spend my pocket money on books.A)for B)but C)so D)or41.George will soon fall behind he finds a better way and applies it to practice.A)because B)when C)until D)unless42.The school aims to encourage people to take a full part in society, it?A)is B)isn't C)does D)doesn't43.-- woman is your English teacher?-- The woman in a red skirtA)Who B)What C)Which D) Whose44.-- .--Sorry. She isn't at home nowA)May I speak to Linda? B)Are you Linda?C)Do you know Linda? D)Can I help you, Linda?45.-- I feel so nervous about the English Speech Competition tomorrow.-- .A)That's cool B) Take it easy. C)Sounds great. D)Glad to hear thatIII. Complete the following passage with the words or phrases in the box. Each word or phrasecan only be used once(将下列单词或词组填入空格。

一、选择题1．若225a =，3b =，则a b +所有可能的值为（ ） A ．8B ．8或2C ．8或2-D ．8±或2±答案：D解析：D 【分析】先求出a 、b 的值，再计算即可． 【详解】 解：∵225a =， ∴a =±5， ∵3b =， ∴b =±3，当a =5，b =3时，8a b +=； 当a =5，b =-3时，2a b +=； 当a =-5，b =3时，2a b +=-； 当a =-5，b =-3时，8a b +=-； 故选：D ． 【点睛】本题考查了绝对值、平方根和有理数加法运算，解题关键是分类讨论，准确计算． 2．正整数n 小于100，并且满足等式236n n n n ⎡⎤⎡⎤⎡⎤++=⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦，其中[]x 表示不超过x 的最大整数，例如：[][]1.5122==，，则满足等式的正整数的个数为（ ） A ．2B ．3C ．12D ．16答案：D解析：D 【分析】利用不等式[x ]≤x 即可求出满足条件的n 的值． 【详解】解：若2n ，3n ，6n有一个不是整数，则22n n ⎡⎤⎢⎥⎣⎦＜或者33n n ⎡⎤⎢⎥⎣⎦＜或者66n n⎡⎤⎢⎥⎣⎦＜， ∴][][236236nn n n n n n ⎡⎤++++=⎢⎥⎣⎦＜，∴2n ，3n ，6n都是整数，即n 是2，3，6的公倍数，且n ＜100， ∴n 的值为6，12，18，24，......96，共有16个，故选：D ． 【点睛】本题主要考查不等式以及取整，关键是要正确理解取整的定义，以及[x ]≤x ＜[x ]+1式子的应用，这个式子在取整中经常用到．3．如图，动点P 在平面直角坐标系中按图中箭头所示方向运动，第一次从原点O 运动到点()11,1P ，第二次运动到点()22,0P ，第三次运动到()33,2P -，…，按这样的运动规律，第2022次运动后，动点2022P 的坐标是（ ）A ．()2022,1B ．()2022,2C ．()2022,2-D ．()2022,0答案：D解析：D 【分析】观察图象，结合动点P 第一次从原点O 运动到点P 1（1，1），第二次运动到点P 2（2，0），第三次运动到P 3（3，﹣2），第四次运动到P 4（4，0），第五运动到P 5（5，2），第六次运动到P 6（6，0），…，结合运动后的点的坐标特点，分别得出点P 运动的纵坐标的规律，再根据循环规律可得答案． 【详解】解：观察图象，结合动点P 第一次从原点O 运动到点P 1（1，1），第二次运动到点P 2（2，0），第三次运动到P 3（3，﹣2），第四次运动到P 4（4，0），第五运动到P 5（5，2），第六次运动到P 6（6，0），…，结合运动后的点的坐标特点， 可知由图象可得纵坐标每6次运动组成一个循环：1，0，﹣2，0，2，0； ∵2022÷6＝337，∴经过第2022次运动后，动点P 的纵坐标是0， 故选：D ． 【点睛】本题考查了规律型点的坐标，数形结合并从图象中发现循环规律是解题的关键． 4．如图，长方形ABCD 中，7AB =，第一次平移长方形ABCD 沿AB 的方向向右平移5个单位，得到长方形1111D C B A ，第3次平移将长方形1111D C B A 沿11A B 的方向向右平移5个单位，得到长方形2222A B C D ，…第n 次平移将长方形1111n n n n A B C D ----的方向平移5个单位，得到长方形(2)n n n n A B C D n >，若n AB 的长度为2022，则n 的值为（ ）A ．403B ．404C ．405D ．406答案：A解析：A 【分析】根据平移的性质得出AA 1=5，A 1A 2=5，A 2B 1=A 1B 1-A 1A 2=7-5=2，进而求出AB 1和AB 2的长，然后根据所求得出数字变化规律，进而得出AB n =（n +1）×5+2求出n 即可． 【详解】解：∵AB =7，第1次平移将长方形ABCD 沿AB 的方向向右平移5个单位，得到长方形A 1B 1C 1D 1，第2次平移将长方形A 1B 1C 1D 1沿A 1B 1的方向向右平移5个单位，得到长方形A 2B 2C 2D 2…， ∴AA 1=5，A 1A 2=5，A 2B 1=A 1B 1-A 1A 2=7-5=2， ∴AB 1=AA 1+A 1A 2+A 2B 1=5+5+2=12， ∴AB 2的长为：5+5+7=17； ∵AB 1=2×5+2=12，AB 2=3×5+2=17， ∴AB n =（n +1）×5+2=2022， 解得：n =403． 故选：A ． 【点睛】此题主要考查了平移的性质以及一元一次方程的应用，根据平移的性质得出AA 1=5，A 1A 2=5是解题关键．5．如图，在平面直角坐标系中，一动点从原点O 出发，按向上，向右，向下，向右的方向不断地移动，每移动一个单位，得到点()1A 0,1，()2A 1,1，()3A 1,0，()4A 2,0，⋯那么点4n 1A (n +为自然数)的坐标为( )(用n 表示)．A ．()2n 1,1-B ．()2n 1,1+C ．()2n,1D ．()4n 1,1+答案：C解析：C 【解析】 【分析】根据图形分别求出n 1=、2、3时对应的点4n 1A +的坐标，然后根据变化规律写出即可．【详解】由图可知，n 1=时，4115⨯+=，点()5A 21，， n 2=时，4219⨯+=，点()9A 41，， n 3=时，43113⨯+=，点()13A 61，， ……所以，点()4n 1A 2n 1+，， 故选C ． 【点睛】本题考查了点的坐标的变化规律，仔细观察图形，分别求出n 1=、2、3时对应的点4n 1A +的对应的坐标是解题的关键．6．如图，已知正方形ABCD ，定点A （1，3），B （1，1），C （3，1），规定“把正方形ABCD 先沿x 轴翻折，再向左平移1个单位长度”为一次变换，如此这样，连续经过2 017次变换后，正方形ABCD 的对角线交点M 的坐标变为（ ）A ．（－2015，2）B ．（－2015，－2）C ．（－2016，－2）D ．（－2016，2）答案：B解析：B 【解析】由正方形ABCD ，顶点A （1，3）、B （1，1）、C （3，1），然后根据题意求得第1次、2次、3次变换后的对角线交点M 的对应点的坐标，即可得规律：第n 次变换后的点M 的对应点的为：当n 为奇数时为（2-n ，-2），当n 为偶数时为（2-n ，2），继而求得把正方形ABCD 连续经过2017次这样的变换得到正方形ABCD 的对角线交点M 的坐标． 解答：∵正方形ABCD ,顶点A (1,3)、B (1,1)、C (3,1). ∴对角线交点M 的坐标为(2,2)，根据题意得：第1次变换后的点M 的对应点的坐标为(2−1,−2),即(1,−2)， 第2次变换后的点M 的对应点的坐标为：(2−2,2),即(0,2)， 第3次变换后的点M 的对应点的坐标为(2−3,−2),即(−1,−2)，第n 次变换后的点M 的对应点的为：当n 为奇数时为(2−n ,−2),当n 为偶数时为(2−n ,2)， ∴连续经过2017次变换后,正方形ABCD 的对角线交点M 的坐标变为(−2015,−2). 故选：B.点睛：本题是一道找规律问题.解题本题的关键在于要通过操作、观察得出操作次数与点的坐标之间的内在联系，并归纳得出符合规律的字母公式.7．在直角坐标系xOy 中，一个质点从()12,A a a 出发沿图中路线依次经过()34,B a a ，()56,C a a ，()78,D a a ，…按此规律一直运动下去，则201920202021a a a ++=（ ）A ．1009B ．1010C ．1011D ．1012答案：B解析：B 【分析】根据题意可得A （1，1），B （-1，2），C （2，3），D （-2，4），E （3，5），F （-3，6），则11a =，21a =，31a =-，42a =，52a =，63a =，72a =-，84a =，由此可知当n 为偶数时2n na =；11a =，31a =-，52a =，72a =-，可得 130a a +=，570a a +=，可以得到21210n n a a -++=，由此求解即可． 【详解】解：由题意可知A （1，1），B （-1，2），C （2，3），D （-2，4），E （3，5），F （-3，6），∴11a =，21a =，31a =-，42a =，52a =，63a =，72a =-，84a =，由此可知当n 为偶数时2n n a = ， ∴2020202010102a == ∵11a =，31a =-，52a =，72a =-，可得 130a a +=，570a a +=， ∴可以得到21210n n a a -++=， ∴201920210a a +=， ∴2019202020211010a a a ++=， 故选B ．【点睛】本题主要考查了点坐标规律的探索，解题的关键在于能够准确找到相应的规律进行求解． 8．如图，在平面直角坐标系中，一动点从原点O 出发，按向上．向右．向下．向右的方向依次平移，每次移动一个单位，得到()10,1A ，()21,1A ，()31,0A ，()42,0A ，…那么点2021A 的坐标为（ ）A ．()505,0B ．()505,1C ．()1010,0D ．()1010,1答案：D解析：D 【分析】根据图象移动的得出移动4次一个循环，得出结果即可； 【详解】根据图象可得移动4次图象完成一个循环， ∵202145051÷=，∴2021A 的坐标是()()5052,11010,1⨯=； 故答案选D ． 【点睛】本题主要考查了点的坐标规律题，准确计算是解题的关键．9．已知{}min ,,a b c 表示取三个数中最小的那个数．例如：当2x =-时，()(){}23min 2,2,28---=-，当{}21min ,,16x x x =时，则x 的值为（ ） A ．116 B ．18C ．14D ．12答案：C解析：C【分析】 本题分别计算2111161616x x x ===，，的x 值，找到满足条件的x 值即可． 【详解】 解：当116x =时，1256x =，x x <，不合题意；当2116x =时，14x =±，当14x =-时，2x x <，不合题意；当14x =时，12x =，2x x x <<，符合题意； 当116x =时，21256x =，2x x <，不合题意， 故选：C ． 【点睛】本题主要考查了实数大小比较，算术平方根及其最值问题，解决此题时，注意分类思想的运用．10．按如图所示的程序计算，若开始输入的值为25，则最后输出的y 值是（ ）A 5B ．5C ．5D ．5±答案：B解析：B 【分析】根据已知进行计算，并判断每一步输出结果即可得到答案． 【详解】解：∵25的算术平方根是5，5不是无理数， ∴再取5的平方根，而5的平方根为5± ∴输出值y ＝5± 故选：B ． 【点睛】本题考查实数分类及计算，判断每步计算结果是否为无理数是解题的关键．11．下列图形都是由同样大小的五角星按一定的规律组成，其中第①个图形一共有2个五角星，第②个图形一共有8个五角星，第③个图形一共有18个五角星，依此类推，则第⑦个图形中五角星的个数是( )A ．98B ．94C ．90D ．86答案：A解析：A 【分析】学会寻找规律，第①个图2个五角星，第②个图形一共有8个五角星，第③个图形一共有18个五角星，那么第n 个图呢，能求出这个即可解得本题。

上海新竹园中学2017学年度七年级第二学期数学周测一 选择题：（每题3分，共18分）1.下列四个式子中，正确的是（ ） 【A 】.981±=【B 】.6=）（6-2-【C 】. 5322=+）（【D 】. 41621= 【答案】D2.下列说法中,正确的是( )【A 】.两条直线被第三条直线所截,同位角相等【B 】.联结直线外一点到直线上各点的所有线段中,垂线最短 【C 】.经过一点,有且只有一条直线与已知直线平行 【D 】.经过一点,有且只有一条直线与已知直线垂直【答案】D【解析】: A 、两条平行线被第三条直线所截,同位角相等,错误;B 、联结直线外一点到直线上各点的所有线段中,垂线段最短,错误;C 、经过直线外一点,有且只有一条直线与已知直线平行,错误;D 、经过一点,有且只有一条直线与已知直线垂直,正确;3. 一副三角板有两个直角三角形，如图叠放在一起，30=∠AED °，45=∠ACB °则BMD ∠的度数是（ ）。

【A】.【B】.【C】.【D】.【答案】A4.如图,OCOC⊥,下面的结论:①OA⊥,ODOA=,ODOB=且OBCD=; ③ABC∠;其中正确的结论( )=CDA∠∆; ②BAAOD∆COB≅【A】.①②【B】.①②③【C】.①③【D】.②③【答案】B5.下列判断中错误的是( )【A】.有两角和一边对应相等的两个三角形全等【B】.有一边对应相等的两个等边三角形全等【C】.有两边和其中一边上的中线对应相等的两个三角形全等【D】.有两边和一角对应相等的两个三角形全等【答案】D6.如图，把△ABC纸片沿DE折叠，当点A落在四边形BCDE的外部时，则∠A与∠1和∠2之间有一种数量关系始终保持不变，请试着找一找这个规律，你发现的规律是（ ）【A 】.∠A=∠1-∠2 【B 】.2∠A=∠1-∠2 【C 】.3∠A=2∠1-∠2 【D 】.3∠A=2（∠1-∠2） 【答案】B二 填空题：（每题3分，共30分） 7.如果的平方根等于，那么______.【答案】168.以线段3、4、5-x 为边组成三角形,则x 的取值范围是 . 【答案】126<<x9. 如图,已知30=∠A °,40=∠B °,50=∠C °,那么=∠AOB 度．【答案】12010.如图，在△ABC 中，AB=4，AC=6，∠ABC 和∠ACB 的平分线交于O 点，过点O 作BC 的平行线交AB 于M 点，交AC 于N 点，则△AMN 的周长为__________． 【答案】1011.如图，在平面上将△ABC 绕点B 旋转到△A ′B ′C ′的位置时，AA ′∥BC ，∠ABC ＝70°，则∠CBC ′的度数为_____ .【答案】40°12.已知点P(0，a)在y 轴的负半轴上，则点Q(12-a -，-a ＋1)在第 象限.【答案】二.13.已知点)53,12(-+m m M 到x 轴的距离是它到y 轴距离的2倍,则m= ．【答案】737或- 14.在平面直角坐标系中，将点（- b ，- a ）称为点（ a ， b ）的“关联点”（例如点（-2，-1）是点（1，2）的“关联点”）．如果一个点和它的“关联点”在同一象限内，那么这一点在第_______象限． 【答案】二或四15.在平面直角坐标系中,点A 的坐标为 ）（1,1,点B 的坐标为 ）（1,11,点C 到直线AB 的距离为4,且 ABC ∆是等腰三角形,则满足条件的点C 有 个. 【答案】1016.如图,在平面直角坐标系中,有若干个整数点,其顺序按图中“”方向排列,如⋯），），（），（），（），（），（（0,31,32,31,20,20,1,根据这个规律探索可得,第100个点的坐标为 ．【答案】）（8,14三 计算题：（每题5分，共20分） 17.32273165131241-----）（）（【答案】-7-3 【解答】解：原式=-4-3-3-2=-7-3 18. 3⨯323612⨯ 【答案】 1 【解答】解：原式=321）（2331⨯1261⨯=119.）（）（）（）（3232867233264131324---- ⨯+⨯+⨯ 【答案】110 【解答】解：原式=）（）（3232163231324131-⨯++=2742⨯+ =11020.化简 44347347-++【答案】6 【解答】解：原式=3232-++设3232-++=x ，则x 2=23232+++-=6，所以x =6即原式=6四 简答题：（每空2分，共10分）21.如图，在直角坐标平面内，已知点A 的坐标为（-5，0）点B 的坐标）（4,3- （1） 点B 关于原点对称的点C 的坐标是 ，点A 关于y 轴对称的点D 的坐标是 ； （2）ABC ∆的面积是 ；（3）在直角坐标平面上找一点E ，能满足S S ABC ADE ∆∆=的E 有 个; （4）在y 轴上找一点F ，当S △ADF =S △ABC 时，点F 的坐标是什么？（用坐标表示，并在图中画出）【答案】（1）C （3，-4），D （5，0）（2）20 （3）无数 （4）（0,4）或（0，-4）【解答】解：（1）根据图形可知点C 的坐标为（3，-4），点D 的坐标为（5，0）；（2）由图可知，S △ABC =S △OAB +S △AOC =21×5×4+21×5×4=20；（3）无数个（4）因为AD=10，所以S △ADF =21AD ·OF=20， 所以OF=4，所以点F 的所有可能位置的坐标是（0，4）或（0，-4）如图所示.五解答题：（22题6分，23题8分，24题8分，共22分）22.已知:如图,BC>AD,DC=DA,BD平分∠ABC,求证:∠A+∠C=180°.【答案】∠A+∠C=180°【解答】解：证明:作DE⊥BA,延长BA与DE交于点E，DF⊥BC.∵BD平分∠ABC,DE⊥BA,DF⊥BC∴DE=DF,又由DC=DA∴Rt△ADE≌Rt△CDF(HL)∴∠C=∠DAE,∵∠DAE+∠A=180°∴∠A+∠C=180°.23.已知:如图1,在等边三角形ABC中,点D、E分别在边AB、BC的延长线上,且CEBD=,联结AE、CD.(1)试说明ACE∆的理由;CBD∆≅(2)如果将CBD∆绕着点B逆时针旋转60°(如图2),此时点C与点A重合,点D落在点G处,联结AG、EG,猜想AEG∆是什么三角形?试说明理由.∆是等边三角形【答案】（1）SAS (2) AEG【解答】解:(1)ABC是等边三角形(已知),∆,(等边三角形的性质).,(邻补角的意义),(等角的补角相等).在CBD ∆和ACE ∆中,ACE CBD ∆≅∆∴(2)猜想:AEG ∆是等边三角形.ABG ∆ 是CBD ∆绕着点B 逆时针旋转得到的,CBD ABG ∆≅∆∴,ACE CBD ∆≅∆ ,, ,,是等腰三角形.,即是等边三角形.24.已知ABC RT ∆中，AC=BC ，∠C=90°，D 为AB 边的中点，∠EDF=90°，∠EDF 绕D 点旋转，它的两边分别交AC 、CB （或它们的延长线）于E 、F ．当∠EDF 绕D 点旋转到DE ⊥AC 于E 时（如图1），易证S S S ABC CEF DEF ∆∆∆=+21．当∠EDF 绕D 点旋转到DE 和AC 不垂直时，在图2和图3这两种情况下，上述结论是否成立? 若成立，请给予证明；若不成立，SDEF∆、SCEF∆、SABC∆又有怎样的数量关系？请写出你的猜想，并证明。

上海民办新竹园中学七年级下册数学期末试卷测试卷（解析版）一、解答题1．如图1，已AB ∥CD ，∠C ＝∠A ． （1）求证：AD ∥BC ；（2）如图2，若点E 是在平行线AB ，CD 内，AD 右侧的任意一点，探究∠BAE ，∠CDE ，∠E 之间的数量关系，并证明．（3）如图3，若∠C ＝90°，且点E 在线段BC 上，DF 平分∠EDC ，射线DF 在∠EDC 的内部，且交BC 于点M ，交AE 延长线于点F ，∠AED +∠AEC ＝180°， ①直接写出∠AED 与∠FDC 的数量关系： ．②点P 在射线DA 上，且满足∠DEP ＝2∠F ，∠DEA ﹣∠PEA ＝514∠DEB ，补全图形后，求∠EPD 的度数2．如图，直线//PQ MN ，一副直角三角板,ABC DEF ∆∆中，90,45,30,60ACB EDF ABC BAC DFE DEF ︒︒︒︒∠=∠=∠=∠=∠=∠=．（1）若DEF ∆如图1摆放，当ED 平分PEF ∠时，证明：FD 平分EFM ∠．（2）若,ABC DEF ∆∆如图2摆放时，则PDE ∠=（3）若图2中ABC ∆固定，将DEF ∆沿着AC 方向平移，边DF 与直线PQ 相交于点G ，作FGQ ∠和GFA ∠的角平分线GH FH 、相交于点H （如图3），求GHF ∠的度数．（4）若图2中DEF ∆的周长35,5cm AF cm =，现将ABC ∆固定，将DEF ∆沿着CA 方向平移至点F 与A 重合，平移后的得到''D E A ∆，点D E 、的对应点分别是''D E 、，请直接写出四边形'DEAD 的周长．（5）若图2中DEF ∆固定，（如图4）将ABC ∆绕点A 顺时针旋转，1分钟转半圈，旋转至AC 与直线AN 首次重合的过程中，当线段BC 与DEF ∆的一条边平行时，请直接写出旋转的时间．3．如图1，点E 在直线AB 、DC 之间，且180DEB ABE CDE ∠+∠-∠=︒． （1）求证：//AB DC ；（2）若点F 是直线BA 上的一点，且BEF BFE ∠=∠，EG 平分DEB ∠交直线AB 于点G ，若20D ∠=︒，求FEG ∠的度数；（3）如图3，点N 是直线AB 、DC 外一点，且满足14CDM CDE ∠=∠，14ABN ABE ∠=∠，ND 与BE 交于点M ．已知()012CDM αα∠=︒<<︒，且//BN DE ，则NMB ∠的度数为______（请直接写出答案，用含α的式子表示）．4．直线AB ∥CD ，点P 为平面内一点，连接AP ，CP ．（1）如图①，点P 在直线AB ，CD 之间，当∠BAP ＝60°，∠DCP ＝20°时，求∠APC 的度数；（2）如图②，点P 在直线AB ，CD 之间，∠BAP 与∠DCP 的角平分线相交于K ，写出∠AKC与∠APC之间的数量关系，并说明理由；（3）如图③，点P在直线CD下方，当∠BAK＝23∠BAP，∠DCK＝23∠DCP时，写出∠AKC与∠APC之间的数量关系，并说明理由．5．已知AB∥CD，∠ABE与∠CDE的角分线相交于点F．（1）如图1，若BM、DM分别是∠ABF和∠CDF的角平分线，且∠BED＝100°，求∠M的度数；（2）如图2，若∠ABM＝13∠ABF，∠CDM＝13∠CDF，∠BED＝α°，求∠M的度数；（3）若∠ABM＝1n∠ABF，∠CDM＝1n∠CDF，请直接写出∠M与∠BED之间的数量关系二、解答题6．问题情境：如图1，AB∥CD，∠PAB=130°，∠PCD=120°，求∠APC的度数．小明的思路是：如图2，过P作PE∥AB，通过平行线性质来求∠APC．（1）按小明的思路，易求得∠APC的度数为度；（2）如图3，AD∥BC，点P在射线OM上运动，当点P在A、B两点之间运动时，∠ADP=∠α，∠BCP=∠β．试判断∠CPD、∠α、∠β之间有何数量关系？请说明理由；（3）在（2）的条件下，如果点P在A、B两点外侧运动时（点P与点A、B、O三点不重合），请你直接写出∠CPD、∠α、∠β间的数量关系．7．如图1，//AB CD ，E 是AB 、CD 之间的一点．（1）判定BAE ∠，CDE ∠与AED ∠之间的数量关系，并证明你的结论；（2）如图2，若BAE ∠、CDE ∠的两条平分线交于点F ．直接写出AFD ∠与AED ∠之间的数量关系；（3）将图2中的射线DC 沿DE 翻折交AF 于点G 得图3，若AGD ∠的余角等于2E ∠的补角，求BAE ∠的大小．8．如图所示，已知//AM BN ，点P 是射线AM 上一动点（与点A 不重合），BC 、BD 分别平分ABP ∠和PBN ∠，分别交射线AM 于点C 、D ，且60CBD ∠=︒ （1）求A ∠的度数．（2）当点P 运动时，APB ∠与ADB ∠之间的数量关系是否随之发生变化？若不变化，请写出它们之间的关系，并说明理由；若变化，请写出变化规律． （3）当点P 运动到使ACB ABD =∠∠时，求ABC ∠的度数．9．已知直线//EF MN ，点,A B 分别为EF ， MN 上的点．（1）如图1，若120FAC ACB ∠=∠=︒，12CAD FAC ∠=∠， 12CBD CBN ∠=∠，求CBN∠与ADB ∠的度数；（2）如图2，若120FAC ACB ∠=∠=︒，13CAD FAC ∠=∠， 13CBD CBN ∠=∠，则ADB =∠_________︒；（3）若把（2）中“120FAC ACB ∠=∠=︒，13CAD FAC ∠=∠， 13CBD CBN ∠=∠”改为“FAC ACB m ∠=∠=︒，1CAD FAC n∠=∠， 1CBD CBN n ∠=∠”，则ADB =∠_________︒．（用含,m n 的式子表示）10．如图1，在平面直角坐标系中，()()02A a C b ，，，，且满足()240a b a b ++-+=，过C 作CB x ⊥轴于B（1）求三角形ABC 的面积．（2）发过B 作//BD AC 交y 轴于D ，且,AE DE 分别平分,CAB ODB ∠∠，如图2，若,90()CAB ACB a αββ∠=∠=+=︒，求AED ∠的度数．（3）在y 轴上是否存在点P ，使得三角形ABC 和三角形ACP 的面积相等？若存在，求出P 点坐标；若不存在；请说明理由．三、解答题11．解读基础：（1）图1形似燕尾，我们称之为“燕尾形”，请写出A ∠、B 、C ∠、D ∠之间的关系，并说明理由；（2）图2形似8字，我们称之为“八字形”，请写出A ∠、B 、C ∠、D ∠之间的关系，并说明理由：应用乐园：直接运用上述两个结论解答下列各题（3）①如图3，在ABC ∆中，BD 、CD 分别平分ABC ∠和ACB ∠，请直接写出A ∠和D ∠的关系 ；②如图4，A B C D E F ∠+∠+∠+∠+∠+∠= ．（4）如图5，BAC ∠与BDC ∠的角平分线相交于点F ，GDC ∠与CAF ∠的角平分线相交于点E ，已知26B ∠=︒，54C ∠=︒，求F ∠和E ∠的度数．12．在ABC 中，射线AG 平分BAC ∠交BC 于点G ，点D 在BC 边上运动（不与点G 重合），过点D 作//DE AC 交AB 于点E .（1）如图1，点D 在线段CG 上运动时，DF 平分EDB ∠.①若100BAC ︒∠=，30C ︒∠=，则AFD ∠=_____；若40B ︒∠=，则AFD ∠=_____； ②试探究AFD ∠与B 之间的数量关系？请说明理由；（2）点D 在线段BG 上运动时，BDE ∠的角平分线所在直线与射线AG 交于点F .试探究AFD ∠与B 之间的数量关系，并说明理由.13．直线MN 与直线PQ 垂直相交于O ，点A 在射线OP 上运动，点B 在射线OM 上运动,A 、B 不与点O 重合，如图1，已知AC 、BC 分别是∠BAP 和∠ABM 角的平分线， （1）点A 、B 在运动的过程中，∠ACB 的大小是否发生变化？若发生变化，请说明理由；若不发生变化，试求出∠ACB 的大小.（2）如图2，将△ABC 沿直线AB 折叠，若点C 落在直线PQ 上，则∠ABO ＝________, 如图3，将△ABC 沿直线AB 折叠，若点C 落在直线MN 上，则∠ABO ＝________ （3）如图4，延长BA 至G ，已知∠BAO 、∠OAG 的角平分线与∠BOQ 的角平分线及其反向延长线交于E 、F ，则∠EAF ＝ ；在△AEF 中，如果有一个角是另一个角的32倍，求∠ABO的度数.14．如果三角形的两个内角α与β满足290αβ+=︒，那么我们称这样的三角形是“准互余三角形”．（1）如图1，在Rt ABC 中，90ACB ∠=︒，BD 是ABC 的角平分线，求证：ABD △是“准互余三角形”；（2）关于“准互余三角形”，有下列说法：①在ABC 中，若100A ∠=︒，70B ∠=︒，10C ∠=︒，则ABC 是“准互余三角形”； ②若ABC 是“准互余三角形”，90C ∠>︒，60A ∠=︒，则20B ∠=︒； ③“准互余三角形”一定是钝角三角形．其中正确的结论是___________（填写所有正确说法的序号）；（3）如图2，B ，C 为直线l 上两点，点A 在直线l 外，且50ABC ∠=︒．若P 是直线l 上一点，且ABP △是“准互余三角形”，请直接写出APB ∠的度数．15．如图①所示，在三角形纸片ABC 中，70C ∠=︒，65B ∠=︒，将纸片的一角折叠，使点A 落在ABC 内的点A '处. （1）若140∠=︒，2∠=________.（2）如图①，若各个角度不确定，试猜想1∠，2∠，A ∠之间的数量关系，直接写出结论. ②当点A 落在四边形BCDE 外部时（如图②），（1）中的猜想是否仍然成立？若成立，请说明理由，若不成立，A ∠，1∠，2∠之间又存在什么关系？请说明．（3）应用：如图③：把一个三角形的三个角向内折叠之后，且三个顶点不重合，那么图∠+∠+∠+∠+∠+∠和是________.中的123456【参考答案】一、解答题1．（1）见解析；（2）∠BAE+∠CDE=∠AED，证明见解析；（3）①∠AED-∠FDC=45°，理由见解析；②50°【分析】（1）根据平行线的性质及判定可得结论；（2）过点E作EF∥AB，根解析：（1）见解析；（2）∠BAE+∠CDE=∠AED，证明见解析；（3）①∠AED-∠FDC=45°，理由见解析；②50°【分析】（1）根据平行线的性质及判定可得结论；（2）过点E作EF∥AB，根据平行线的性质得AB∥CD∥EF，然后由两直线平行内错角相等可得结论；（3）①根据∠AED+∠AEC=180°，∠AED+∠DEC+∠AEB=180°，DF平分∠EDC，可得出2∠AED+（90°-2∠FDC）=180°，即可导出角的关系；②先根据∠AED=∠F+∠FDE，∠AED-∠FDC=45°得出∠DEP=2∠F=90°，再根据∠DEA-∠PEA=5∠DEB，求出∠AED=50°，即可得出∠EPD的度数．14【详解】解：（1）证明：AB∥CD，∴∠A+∠D=180°，∵∠C=∠A，∴∠C+∠D=180°，∴AD∥BC；（2）∠BAE+∠CDE=∠AED，理由如下：如图2，过点E作EF∥AB，∵AB∥CD∴AB∥CD∥EF∴∠BAE=∠AEF，∠CDE=∠DEF即∠FEA+∠FED=∠CDE+∠BAE∴∠BAE+∠CDE=∠AED；（3）①∠AED-∠FDC=45°；∵∠AED+∠AEC=180°，∠AED+∠DEC+∠AEB=180°，∴∠AEC=∠DEC+∠AEB，∴∠AED=∠AEB，∵DF平分∠EDC∠DEC=2∠FDC∴∠DEC=90°-2∠FDC，∴2∠AED+（90°-2∠FDC）=180°，∴∠AED-∠FDC=45°，故答案为：∠AED-∠FDC=45°；②如图3，∵∠AED=∠F+∠FDE，∠AED-∠FDC=45°，∴∠F=45°，∴∠DEP=2∠F=90°，∵∠DEA-∠PEA=514∠DEB=57∠DEA，∴∠PEA=2∠AED，7∠AED=90°，∴∠DEP=∠PEA+∠AED=97∴∠AED=70°，∵∠AED+∠AEC=180°，∴∠DEC+2∠AED=180°，∴∠DEC=40°，∵AD∥BC，∴∠ADE=∠DEC=40°，在△PDE中，∠EPD=180°-∠DEP-∠AED=50°，即∠EPD=50°．【点睛】本题主要考查平行线的判定和性质，熟练掌握平行线的判定和性质，角平分线的性质等知识点是解题的关键．2．（1）见详解；（2）15°；（3）67.5°；（4）45cm；（5）10s或30s或40s 【分析】（1）运用角平分线定义及平行线性质即可证得结论；（2）如图2，过点E作EK∥MN，利用平行线性解析：（1）见详解；（2）15°；（3）67.5°；（4）45cm；（5）10s或30s或40s【分析】（1）运用角平分线定义及平行线性质即可证得结论；（2）如图2，过点E作EK∥MN，利用平行线性质即可求得答案；（3）如图3，分别过点F、H作FL∥MN，HR∥PQ，运用平行线性质和角平分线定义即可得出答案；（4）根据平移性质可得D′A＝DF，DD′＝EE′＝AF＝5cm，再结合DE＋EF＋DF＝35cm，可得出答案；（5）设旋转时间为t秒，由题意旋转速度为1分钟转半圈，即每秒转3°，分三种情况：①当BC∥DE时，②当BC∥EF时，③当BC∥DF时，分别求出旋转角度后，列方程求解即可．【详解】（1）如图1，在△DEF中，∠EDF＝90°，∠DFE＝30°，∠DEF＝60°，∵ED平分∠PEF，∴∠PEF＝2∠PED＝2∠DEF＝2×60°＝120°，∵PQ∥MN，∴∠MFE＝180°−∠PEF＝180°−120°＝60°，∴∠MFD＝∠MFE−∠DFE＝60°−30°＝30°，∴∠MFD＝∠DFE，∴FD平分∠EFM；（2）如图2，过点E作EK∥MN，∵∠BAC＝45°，∴∠KEA＝∠BAC＝45°，∵PQ∥MN，EK∥MN，∴PQ∥EK，∴∠PDE＝∠DEK＝∠DEF−∠KEA，又∵∠DEF＝60°．∴∠PDE＝60°−45°＝15°，故答案为：15°；（3）如图3，分别过点F、H作FL∥MN，HR∥PQ，∴∠LFA＝∠BAC＝45°，∠RHG＝∠QGH，∵FL∥MN，HR∥PQ，PQ∥MN，∴FL∥PQ∥HR，∴∠QGF＋∠GFL＝180°，∠RHF＝∠HFL＝∠HFA−∠LFA，∵∠FGQ和∠GFA的角平分线GH、FH相交于点H，∴∠QGH＝12∠FGQ，∠HFA＝12∠GFA，∵∠DFE＝30°，∴∠GFA＝180°−∠DFE＝150°，∴∠HFA＝12∠GFA＝75°，∴∠RHF＝∠HFL＝∠HFA−∠LFA＝75°−45°＝30°，∴∠GFL＝∠GFA−∠LFA＝150°−45°＝105°，∴∠RHG＝∠QGH＝12∠FGQ＝12（180°−105°）＝37.5°，∴∠GHF＝∠RHG＋∠RHF＝37.5°＋30°＝67.5°；（4）如图4，∵将△DEF沿着CA方向平移至点F与A重合，平移后的得到△D′E′A，∴D′A＝DF，DD′＝EE′＝AF＝5cm，∵DE＋EF＋DF＝35cm，∴DE＋EF＋D′A＋AF＋DD′＝35＋10＝45（cm），即四边形DEAD′的周长为45cm；（5）设旋转时间为t秒，由题意旋转速度为1分钟转半圈，即每秒转3°，分三种情况：BC∥DE时，如图5，此时AC∥DF，∴∠CAE＝∠DFE＝30°，∴3t＝30，解得：t＝10；BC∥EF时，如图6，∵BC∥EF，∴∠BAE＝∠B＝45°，∴∠BAM＝∠BAE＋∠EAM＝45°＋45°＝90°，∴3t＝90，解得：t＝30；BC∥DF时，如图7，延长BC交MN于K，延长DF交MN于R，∵∠DRM＝∠EAM＋∠DFE＝45°＋30°＝75°，∴∠BKA＝∠DRM＝75°，∵∠ACK＝180°−∠ACB＝90°，∴∠CAK＝90°−∠BKA＝15°，∴∠CAE＝180°−∠EAM−∠CAK＝180°−45°−15°＝120°，∴3t＝120，解得：t ＝40，综上所述，△ABC 绕点A 顺时针旋转的时间为10s 或30s 或40s 时，线段BC 与△DEF 的一条边平行．【点睛】本题主要考查了平行线性质及判定，角平分线定义，平移的性质等，添加辅助线，利用平行线性质是解题关键．3．（1）见解析；（2）10°；（3）【分析】（1）过点E 作EF ∥CD ，根据平行线的性质，两直线平行，内错角相等，得出结合已知条件，得出即可证明；（2）过点E 作HE ∥CD ，设 由（1）得AB ∥CD解析：（1）见解析；（2）10°；（3）18015α︒-【分析】（1）过点E 作EF ∥CD ，根据平行线的性质，两直线平行，内错角相等，得出,CDE DEF ∠=∠结合已知条件180DEB ABE CDE ∠+∠-∠=︒，得出180,FEB ABE ∠+∠=︒即可证明；（2）过点E 作HE ∥CD ，设,,GEF x FEB EFB y ∠=∠=∠= 由（1）得AB ∥CD ，则AB ∥CD ∥HE ，由平行线的性质，得出20,DEF D EFB y ∠=∠+∠=︒+再由EG 平分DEB ∠，得出,DEG GEB GEF FEB x y ∠=∠=∠+∠=+则2DEF DEG GEF x y ∠=∠+∠=+，则可列出关于x 和y 的方程，即可求得x ，即GEF ∠的度数；（3）过点N 作NP ∥CD ，过点M 作QM ∥CD ，由（1）得AB ∥CD ，则NP ∥CD ∥AB ∥QM ，根据14CDM CDE ∠=∠和CDM α∠=，得出3,MDE α∠=根据CD ∥PN ∥QM ,DE ∥NB ,得出,PND CDM DMQ α∠=∠=∠=3,EDM BNM α∠=∠=即4,BNP α∠=根据NP ∥AB ，得出4,PNB ABN α∠=∠=再由14ABN ABE ∠=∠，得出16,ABM α∠=由AB ∥QM ,得出18016,QMB α∠=︒-因为NMB NMQ QMB ∠=∠+∠，代入α的式子即可求出BMN ∠．【详解】（1）过点E 作EF ∥CD ，如图，∵EF ∥CD ,∴,CDE DEF ∠=∠∴,DEB CDE DEB DEF FEB ∠-∠=∠-∠=∠∵180DEB ABE CDE ∠+∠-∠=︒,∴180,FEB ABE ∠+∠=︒∴EF ∥AB ，∴CD ∥AB ；（2）过点E 作HE ∥CD ，如图，设,,GEF x FEB EFB y ∠=∠=∠=由（1）得AB ∥CD ，则AB ∥CD ∥HE ，∴20,,D DEH HEF EFB y ∠=∠=︒∠=∠=∴20,DEF DEH HEF D EFB y ∠=∠+∠=∠+∠=︒+又∵EG 平分DEB ∠，∴,DEG GEB GEF FEB x y ∠=∠=∠+∠=+∴2,DEF DEG GEF x y x x y ∠=∠+∠=++=+即220,x y y +=︒+解得：10,x =︒即10GEF ∠=︒；（3）过点N 作NP ∥CD ，过点M 作QM ∥CD ，如图，由（1）得AB ∥CD ，则NP ∥CD ∥AB ∥QM ，∵NP ∥CD ，CD ∥QM ，,CDM α∠=∴PND CDM DMQ α∠=∠=∠=,又∵14CDM CDE ∠=∠， ∴33,MDE CDM α∠=∠=∵//BN DE ,∴3,MDE BNM α∠=∠=∴34,PNB PND BNM ααα∠=∠+∠=+=又∵PN ∥AB ，∴4,PNB NBA α∠=∠= ∵14ABN ABE ∠=∠,∴44416,ABM ABN αα∠=∠=⨯=又∵AB ∥QM ，∴180,ABM QMB ∠+∠=︒∴18018016,QMB ABM α∠=︒-∠=︒-∴1801618015NMB NMQ QMB ααα∠=∠+∠=+︒-=-．【点睛】本题考查平行线的性质，角平分线的定义，解决问题的关键是作平行线构造相等的角，利用两直线平行，内错角相等，同位角相等来计算和推导角之间的关系．4．（1）80°；（2）∠AKC ＝∠APC ，理由见解析；（3）∠AKC ＝∠APC ，理由见解析【分析】（1）先过P 作PE ∥AB ，根据平行线的性质即可得到∠APE ＝∠BAP ，∠CPE ＝∠DCP ，再根据∠解析：（1）80°；（2）∠AKC ＝12∠APC ，理由见解析；（3）∠AKC ＝23∠APC ，理由见解析【分析】（1）先过P 作PE ∥AB ，根据平行线的性质即可得到∠APE ＝∠BAP ，∠CPE ＝∠DCP ，再根据∠APC ＝∠APE +∠CPE ＝∠BAP +∠DCP 进行计算即可；（2）过K 作KE ∥AB ，根据KE ∥AB ∥CD ，可得∠AKE ＝∠BAK ，∠CKE ＝∠DCK ，进而得到∠AKC ＝∠AKE +∠CKE ＝∠BAK +∠DCK ，同理可得，∠APC ＝∠BAP +∠DCP ，再根据角平分线的定义，得出∠BAK +∠DCK ＝12∠BAP +12∠DCP ＝12（∠BAP +∠DCP ）＝12∠APC ，进而得到∠AKC ＝12∠APC ；（3）过K 作KE ∥AB ，根据KE ∥AB ∥CD ，可得∠BAK ＝∠AKE ，∠DCK ＝∠CKE ，进而得到∠AKC ＝∠BAK ﹣∠DCK ，同理可得，∠APC ＝∠BAP ﹣∠DCP ，再根据已知得出∠BAK ﹣∠DCK ＝23∠BAP ﹣23∠DCP ＝23∠APC ，进而得到∠BAK ﹣∠DCK ＝23∠APC ． 【详解】（1）如图1，过P 作PE ∥AB ，∵AB ∥CD ，∴PE ∥AB ∥CD ，∴∠APE ＝∠BAP ，∠CPE ＝∠DCP ，∴∠APC ＝∠APE +∠CPE ＝∠BAP +∠DCP ＝60°+20°＝80°；（2）∠AKC ＝12∠APC ．理由：如图2，过K 作KE ∥AB ，∵AB ∥CD ，∴KE ∥AB ∥CD ，∴∠AKE ＝∠BAK ，∠CKE ＝∠DCK ，∴∠AKC＝∠AKE+∠CKE＝∠BAK+∠DCK，过P作PF∥AB，同理可得，∠APC＝∠BAP+∠DCP，∵∠BAP与∠DCP的角平分线相交于点K，∴∠BAK+∠DCK＝12∠BAP+12∠DCP＝12（∠BAP+∠DCP）＝12∠APC，∴∠AKC＝12∠APC；（3）∠AKC＝23∠APC理由：如图3，过K作KE∥AB，∵AB∥CD，∴KE∥AB∥CD，∴∠BAK＝∠AKE，∠DCK＝∠CKE，∴∠AKC＝∠AKE﹣∠CKE＝∠BAK﹣∠DCK，过P作PF∥AB，同理可得，∠APC＝∠BAP﹣∠DCP，∵∠BAK＝23∠BAP，∠DCK＝23∠DCP，∴∠BAK﹣∠DCK＝23∠BAP﹣23∠DCP＝23（∠BAP﹣∠DCP）＝23∠APC，∴∠AKC＝23∠APC．【点睛】本题考查了平行线的性质和角平分线的定义，解题的关键是作出平行线构造内错角相等计算．5．（1）65°；（2）；（3）2n∠M+∠BED=360°【分析】（1）首先作EG∥AB，FH∥AB，连结MF，利用平行线的性质可得∠ABE+∠CDE=260°，再利用角平分线的定义得到∠ABF+解析：（1）65°；（2）3606α︒-︒；（3）2n∠M+∠BED=360°【分析】（1）首先作EG∥AB，FH∥AB，连结MF，利用平行线的性质可得∠ABE+∠CDE=260°，再利用角平分线的定义得到∠ABF+∠CDF=130°，从而得到∠BFD的度数，再根据角平分线的定义和三角形外角的性质可求∠M的度数；（2）先由已知得到∠ABE=6∠ABM，∠CDE=6∠CDM，由（1）得∠ABE+∠CDE=360°-∠BED ，∠M =∠ABM +∠CDM ，等量代换即可求解；（3）由（2）的方法可得到2n ∠M +∠BED =360°．【详解】解：（1）如图1，作//EG AB ，//FH AB ，连结MF ，//AB CD ，//////EG AB FH CD ∴，ABF BFH ∴∠=∠，CDF DFH ∠=∠，180ABE BEG ∠+∠=︒，180GED CDE ∠+∠=︒， 360ABE BEG GED CDE ∴∠+∠+∠+∠=︒，100BED BEG DEG ∠=∠+∠=︒，260ABE CDE ∴∠+∠=︒，ABE ∠和CDE ∠的角平分线相交于E ，130ABF CDF ∴∠+∠=︒，130BFD BFH DFH ∴∠=∠+∠=︒， BM 、DM 分别是ABF ∠和CDF ∠的角平分线，12MBF ABF ∴∠=∠，12MDF CDF ∠=∠， 65MBF MDF ∴∠+∠=︒，1306565BMD ∴∠=︒-︒=︒；（2）如图1，13ABM ABF ∠=∠，13CDM CDF ∠=∠， 3ABF ABM ∴∠=∠，3CDF CDM ∠=∠，ABE ∠与CDE ∠两个角的角平分线相交于点F ，6ABE ABM ∴∠=∠，6CDE CDM ∠=∠，66360ABM CDM BED ∴∠+∠+∠=︒，BMD ABM CDM ∠=∠+∠，6360BMD BED ∴∠+∠=︒，3606BMD α︒-︒∴∠=； （3）由（2）结论可得，22360n ABM n CDM E ∠+∠+∠=︒，M ABM CDM ∠=∠+∠， 则2360n M BED ∠+∠=︒．【点睛】本题主要考查了平行线的性质和四边形的内角和，关键在于掌握两直线平行同位角相等，内错角相等，同旁内角互补的性质．二、解答题6．（1）110°；（2）∠CPD=∠α+∠β，见解析；（3）当P 在BA 延长线时，∠CPD=∠β-∠α；当P在AB延长线上时，∠CPD=∠α-∠β【分析】（1）过P作PE∥AB，通过平行线性质求∠A解析：（1）110°；（2）∠CPD=∠α+∠β，见解析；（3）当P在BA延长线时，∠CPD=∠β-∠α；当P在AB延长线上时，∠CPD=∠α-∠β【分析】（1）过P作PE∥AB，通过平行线性质求∠APC即可；（2）过P作PE∥AD交CD于E，推出AD∥PE∥BC，根据平行线的性质得出∠α=∠DPE，∠β=∠CPE，即可得出答案；（3）画出图形，根据平行线的性质得出∠α=∠DPE，∠β=∠CPE，即可得出答案．【详解】解：（1）过点P作PE∥AB，∵AB∥CD，∴PE∥AB∥CD，∴∠A+∠APE=180°，∠C+∠CPE=180°，∵∠PAB=130°，∠PCD=120°，∴∠APE=50°，∠CPE=60°，∴∠APC=∠APE+∠CPE=110°．故答案为110°；（2）∠CPD=∠α+∠β，理由是：如图3，过P作PE∥AD交CD于E，∵AD∥BC，∴AD∥PE∥BC，∴∠α=∠DPE，∠β=∠CPE，∴∠CPD=∠DPE+∠CPE=∠α+∠β；（3）当P在BA延长线时，∠CPD=∠β-∠α，理由是：如图4，过P作PE∥AD交CD于E，∵AD ∥BC ，∴AD ∥PE ∥BC ，∴∠α=∠DPE ，∠β=∠CPE ，∴∠CPD =∠CPE-∠DPE =∠β-∠α；当P 在AB 延长线时，∠CPD =∠α-∠β，理由是：如图5，过P 作PE ∥AD 交CD 于E ，∵AD ∥BC ，∴AD ∥PE ∥BC ，∴∠α=∠DPE ，∠β=∠CPE ，∴∠CPD =∠DPE -∠CPE =∠α-∠β．【点睛】本题考查了平行线的性质和判定的应用，主要考查学生的推理能力，题目是一道比较典型的题目，分类讨论是解题的关键．7．（1），见解析；（2）；（3）60°【分析】（1）作EF//AB ，如图1，则EF//CD ，利用平行线的性质得∠1＝∠BAE ，∠2＝∠CDE ，从而得到∠BAE ＋∠CDE ＝∠AED ；（2）如图2，解析：（1）BAE CDE AED ∠+∠=∠，见解析；（2）12AFD AED ∠=∠；（3）60° 【分析】（1）作EF //AB ，如图1，则EF //CD ，利用平行线的性质得∠1＝∠BAE ，∠2＝∠CDE ，从而得到∠BAE ＋∠CDE ＝∠AED ；（2）如图2，由（1）的结论得∠AFD ＝∠BAF ＋∠CDF ，根据角平分线的定义得到∠BAF ＝12∠BAE ，∠CDF ＝12∠CDE ，则∠AFD ＝12（∠BAE ＋∠CDE ），加上（1）的结论得到∠AFD ＝12∠AED ；（3）由（1）的结论得∠AGD ＝∠BAF ＋∠CDG ，利用折叠性质得∠CDG ＝4∠CDF ，再利用等量代换得到∠AGD ＝2∠AED －32∠BAE ，加上90°－∠AGD ＝180°－2∠AED ，从而可计算出∠BAE 的度数． 【详解】解：（1）BAE CDE AED ∠+∠=∠ 理由如下： 作//EF AB ，如图1，//AB CD ，//EF CD ∴．1BAE ∴∠=∠，2CDE ∠=∠，BAE CDE AED ∴∠+∠=∠；（2）如图2，由（1）的结论得AFD BAF CDF ∠=∠+∠， BAE ∠、CDE ∠的两条平分线交于点F ，12BAF BAE ∴∠=∠，12CDF CDE ∠=∠，1()2AFD BAE CDE ∴∠=∠+∠，BAE CDE AED ∠+∠=∠，12AFD AED ∴∠=∠；（3）由（1）的结论得AGD BAF CDG ∠=∠+∠， 而射线DC 沿DE 翻折交AF 于点G ，4CDG CDF ∴∠=∠，11422()22AGD BAF CDF BAE CDE BAE AED BAE ∴∠=∠+∠=∠+∠=∠+∠-∠=322AED BAE ∠-∠，901802AGD AED ︒-∠=︒-∠，390218022AED BAE AED ∴︒-∠+∠=︒-∠，60BAE ∴∠=︒．【点睛】本题考查了平行线性质：两直线平行，同位角相等；两直线平行，同旁内角互补；两直线平行，内错角相等．8．（1）；（2）不变化，，理由见解析；（3） 【分析】（1）结合题意，根据角平分线的性质，得；再根据平行线的性质计算，即可得到答案；（2）根据平行线的性质，得，；结合角平分线性质，得，即可完成求解解析：（1）60A ∠=；（2）不变化，2APB ADB ∠=∠，理由见解析；（3）30ABC ∠= 【分析】（1）结合题意，根据角平分线的性质，得ABN ∠；再根据平行线的性质计算，即可得到答案；（2）根据平行线的性质，得APB PBN ∠=∠，ADB DBN ∠=∠；结合角平分线性质，得2APB ADB ∠=∠，即可完成求解；（3）根据平行线的性质，得ACB CBN ∠=∠；结合ACB ABD =∠∠，推导得ABC DBN ∠=∠；再结合（1）的结论计算，即可得到答案．【详解】（1）∵BC ，BD 分别评分ABP ∠和PBN ∠， ∴1122CBP ABP DBP PBN ∠=∠∠=∠，，∴2ABN CBD ∠=∠ 又∵60CBD ∠=， ∴120ABN ∠= ∵//AM BN ， ∴180A ABN ∠+∠= ∴60A ∠=； （2）∵//AM BN ，∴APB PBN ∠=∠，ADB DBN ∠=∠ 又∵BD 平分PBN ∠ ∴2PBN DBN ∠=∠， ∴2APB ADB ∠=∠；∴APB ∠与ADB ∠之间的数量关系保持不变； （3）∵//AD BN ， ∴ACB CBN ∠=∠ 又∵ACB ABD =∠∠， ∴CBN ABD ∠=∠，∵ABC CBN ABD DBN ∠+∠=∠+∠ ∴ABC DBN ∠=∠由（1）可得60CBD ∠=，120ABN ∠=∴()112060302ABC ∠=⨯-=．【点睛】本题考查了角平分线、平行线的知识；解题的关键是熟练掌握角平分线、平行线的性质，从而完成求解．9．（1）120º，120º；（2）160；（3） 【分析】（1）过点作，，根据 ，平行线的性质和周角可求出，则 ，再根据 ， ，可得 ， ，可求出 ，，根据 即可得到结果； （2）同理（1）的求法，解析：（1）120º，120º；（2）160；（3）()1360n m n-⋅- 【分析】（1）过点,C D 作CGEF ，DH EF ，根据 120FAC ACB ∠=∠=︒，平行线的性质和周角可求出120GCB ∠=︒，则 120CBN GCB ∠=∠=︒，再根据 12CAD FAC ∠=∠，12CBD CBN ∠=∠，可得 1602CBD CBN ∠=∠=︒， 1602CAD FAC ∠=∠=︒，可求出60ADH FAD ∠=∠=︒，60BDH DBN ∠=∠=︒，根据 ADB ADH BDH ∠=∠+∠即可得到结果；（2）同理（1）的求法，根据120FAC ACB ∠=∠=︒，13CAD FAC ∠=∠，13CBD CBN ∠=∠求解即可；（3）同理（1）的求法，根据FAC ACB m ∠=∠=︒，1CAD FAC n∠=∠， 1CBD CBNn ∠=∠求解即可； 【详解】解：（1）如图示，分别过点,C D 作CGEF ，DH EF ，∵EF MN ， ∴EFMNCGDH ，∴120ACG FAC ∠=∠=︒，∴360120GCB ACG ACB ∠=︒-∠-∠=︒， ∴120CBN GCB ∠=∠=︒，∵1602CBD CBN ∠=∠=︒， 1602CAD FAC ∠=∠=︒∴60DBN CBN CBD ∠=∠-∠=︒， 又∵60FAD FAC CAD ∠=∠-∠=︒，∴60ADH FAD ∠=∠=︒，60BDH DBN ∠=∠=︒， ∴120ADB ADH BDH ∠=∠+∠=︒． （2）如图示，分别过点,C D 作CGEF ，DH EF ，∵EF MN ，∴EFMN CGDH ，∴120ACG FAC ∠=∠=︒，∴360120GCB ACG ACB ∠=︒-∠-∠=︒， ∴120CBN GCB ∠=∠=︒，∵1403CBD CBN ∠=∠=︒， 1403CAD FAC ∠=∠=︒ ∴80DBN CBN CBD ∠=∠-∠=︒， 又∵80FAD FAC CAD ∠=∠-∠=︒，∴80ADH FAD ∠=∠=︒，80BDH DBN ∠=∠=︒， ∴160ADB ADH BDH ∠=∠+∠=︒． 故答案为：160； （3）同理（1）的求法 ∵EFMN ，∴EFMNCGDH ，∴ACG FAC m ∠=∠=︒，∴3603602GCB ACG ACB m ∠=︒-∠-∠=︒-︒， ∴3602CBN GCB m ∠=∠=︒-︒， ∵13602m CBD CBN nn ︒-︒∠=∠=， 1m CAD FAC n n︒∠=∠= ∴()()360213602=3602m n m DBN CB D m nN n CB ︒-︒-︒-︒-︒∠-∠=-=∠︒， 又∵()1n m FAD FAC CAD m m n n-︒∠=∠-∠=︒-=︒，∴()1n ADH FAD m n-∠=∠=︒， ()13602n BDH DBN m n-∠=∠=︒-︒，∴()()()1113602=360n n n ADB ADH BDH m m m nn n--∠=∠+∠=-︒︒-︒︒-+︒． 故答案为：()1360n m n-⋅-． 【点睛】本题主要考查了平行线的性质和角度的运算，熟悉相关性质是解题的关键．10．（1）4；（2）45°；（3）P （0，－1）或（0，3） 【分析】（1）根据非负数的性质得到a ＝−b ，a−b ＋4＝0，解得a ＝−2，b ＝2，则A （−2，0），B （2，0），C （2，2），即可计算出解析：（1）4；（2）45°；（3）P （0，－1）或（0，3） 【分析】（1）根据非负数的性质得到a ＝−b ，a−b ＋4＝0，解得a ＝−2，b ＝2，则A （−2，0），B （2，0），C （2，2），即可计算出三角形ABC 的面积＝4；（2）由于CB ∥y 轴，BD ∥AC ，则∠CAB ＝∠ABD ，即∠3＋∠4＋∠5＋∠6＝90°，过E 作EF ∥AC ，则BD ∥AC ∥EF ，然后利用角平分线的定义可得到∠3＝∠4＝∠1，∠5＝∠6＝∠2，所以∠AED ＝∠1＋∠2＝12×90°＝45°；（3）先根据待定系数法确定直线AC 的解析式为y ＝12x ＋1，则G 点坐标为（0，1），然后利用S △PAC ＝S △APG ＋S △CPG 进行计算． 【详解】解：（1）由题意知：a ＝−b ，a−b ＋4＝0， 解得：a ＝−2，b ＝2，∴ A （−2，0），B （2，0），C （2，2）， ∴S △ABC ＝1AB BC=42⋅；（2）∵CB ∥y 轴，BD ∥AC ， ∴∠CAB ＝∠ABD ，∴∠3＋∠4＋∠5＋∠6＝90°， 过E 作EF ∥AC ，∵BD ∥AC ， ∴BD ∥AC ∥EF ，∵AE ，DE 分别平分∠CAB ，∠ODB ， ∴∠3＝∠4＝∠1，∠5＝∠6＝∠2，∴∠AED ＝∠1＋∠2＝12×90°＝45°； （3）存在．理由如下：设P 点坐标为（0，t ），直线AC 的解析式为y ＝kx ＋b ， 把A （−2，0）、C （2，2）代入得：-2k+b=02k+b=2⎧⎨⎩，解得1k=2b=1⎧⎪⎨⎪⎩， ∴直线AC 的解析式为y ＝12x ＋1， ∴G 点坐标为（0，1），∴S △PAC ＝S △APG ＋S △CPG ＝12|t−1|•2＋12|t−1|•2＝4，解得t ＝3或−1， ∴P 点坐标为（0，3）或（0，−1）．【点睛】本题考查了绝对值、平方的非负性，平行线的判定与性质：内错角相等，两直线平行；同旁内角互补，两直线平行；两直线平行，内错角相等．三、解答题11．（1），理由详见解析；（2），理由详见解析：（3）①；②360°；（4）； . 【分析】（1）根据三角形外角等于不相邻的两个内角之和即可得出结论； （2）根据三角形内角和定理及对顶角相等即可得出结解析：（1）D A B C ∠=∠+∠+∠，理由详见解析；（2）A D B C ∠+∠=∠+∠，理由详见解析：（3）①1902D A ∠=︒+∠；②360°；（4）124E ∠=︒； =14F ∠︒. 【分析】（1）根据三角形外角等于不相邻的两个内角之和即可得出结论； （2）根据三角形内角和定理及对顶角相等即可得出结论； （3）①根据角平分线的定义及三角形内角和定理即可得出结论； ②连结BE ，由（2）的结论及四边形内角和为360°即可得出结论；（4）根据（1）的结论、角平分线的性质以及三角形内角和定理即可得出结论． 【详解】（1）D A B C ∠=∠+∠+∠．理由如下：如图1，BDE B BAD ∠=∠+∠，CDE C CAD ∠=∠+∠，BDC B BAD C CAD B BAC C ∴∠=∠+∠+∠+∠=∠+∠+∠，D A B C ∴∠=∠+∠+∠；（2）A D B C ∠+∠=∠+∠．理由如下：在ADE ∆中，180AED A D ∠=︒-∠-∠，在BCE ∆中，180BEC B C ∠=︒-∠-∠，AED BEC ∠=∠，A D B C ∴∠+∠=∠+∠；（3）①180A ABC ACB ∠=︒-∠-∠，180D DBC DCB ∠=︒-∠-∠，BD 、CD 分别平分ABC∠和ACB ∠，∴1122ABC ACB DBC DCB ∠+∠=∠+∠，1111180()180(180)902222D ABC ACB A A ∴∠=︒-∠+∠=︒-︒-∠=︒+∠．故答案为：1902D A ∠=︒+∠． ②连结BE ． ∵C D CBE DEB ∠+∠=∠+∠，360A B C D E F A ABE F BEF ∴∠+∠+∠+∠+∠+∠=∠+∠+∠+∠=︒．故答案为：360︒；（4）由（1）知，BDC B C BAC ∠=∠+∠+∠，26B ∠=︒，54C ∠=︒，80BDC BAC ∴∠=︒+∠，402CDF CAE ∴∠=︒+∠，4BAC CAE ∠=∠，2BDC CDF ∠=∠，1902GDE CDF ∴∠=︒-∠，26180AGD B GDB CDF ∠=∠+∠=︒+︒-∠，3GAE CAE ∠=∠，3336064(2)644012422E GAE AGD GDE CAE CDF ∴∠=︒-∠-∠-∠=︒-∠-∠=︒+⨯︒=︒；180180(206)2262264014F AGF GAF CDF CAE CDF CAE ∠=︒-∠-∠=︒-︒-∠-∠=-︒+∠-∠=-︒+︒=︒． 【点睛】本题考查了角平分线的性质，三角形内角和；熟练掌握角平分线的性质，进行合理的等量代换是解题的关键．12．（1）①115°，110°；②，证明见解析；（2），证明见解析. 【解析】 【分析】（1）①根据角平分线的定义求得∠CAG=∠BAC=50°；再由平行线的性质可得∠EDG=∠C=30°，∠FMD=解析：（1）①115°，110°；②1902AFD B ︒∠=+∠，证明见解析；（2）1902AFD B ︒∠=-∠，证明见解析.【解析】【分析】（1）①根据角平分线的定义求得∠CAG=12∠BAC=50°；再由平行线的性质可得∠EDG=∠C=30°，∠FMD=∠GAC=50°；由三角形的内角和定理求得∠AFD的度数即可；已知AG平分∠BAC，DF平分∠EDB，根据角平分线的定义可得∠CAG=12∠BAC，∠FDM=12∠EDG；由DE//AC，根据平行线的性质可得∠EDG=∠C，∠FMD=∠GAC；即可得∠FDM +∠FMD=12∠EDG +∠GAC=12∠C+12∠BAC=12（∠BAC+∠C）=12×140°=70°；再由三角形的内角和定理可求得∠AFD=110°；②∠AFD=90°+12∠B，已知AG平分∠BAC，DF平分∠EDB，根据角平分线的定义可得∠CAG=12∠BAC，∠FDM=12∠EDG；由DE//AC，根据平行线的性质可得∠EDG=∠C，∠FMD=∠GAC；由此可得∠FDM +∠FMD=12∠EDG +∠GAC=12∠C+12∠BAC=12（∠BAC+∠C）=12×（180°-∠B）=90°-12∠B；再由三角形的内角和定理可得∠AFD=90°+12∠B；（2）∠AFD=90°-12∠B，已知AG平分∠BAC，DF平分∠EDB，根据角平分线的定义可得∠CAG=12∠BAC，∠NDE=12∠EDB，即可得∠FDM=∠NDE=12∠EDB；由DE//AC，根据平行线的性质可得∠EDB=∠C，∠FMD=∠GAC；即可得到∠FDM=∠NDE=12∠C，所以∠FDM+∠FMD =12∠C+12∠BAC=12（∠BAC+∠C）=12×（180°-∠B）=90°-12∠B；再由三角形外角的性质可得∠AFD=∠FDM +∠FMD=90°-12∠B.【详解】（1）①∵AG平分∠BAC，∠BAC=100°，∴∠CAG=12∠BAC=50°；∵//DE AC，∠C=30°，∴∠EDG=∠C=30°，∠FMD=∠GAC=50°；∵DF平分∠EDB，∴∠FDM=12∠EDG=15°；∴∠AFD=180°-∠FMD-∠FDM=180°-50°-15°=115°；∵∠B=40°，∴∠BAC+∠C=180°-∠B=140°；∵AG平分∠BAC，DF平分∠EDB，∴∠CAG=12∠BAC，∠FDM=12∠EDG，∵DE//AC，∴∠EDG=∠C，∠FMD=∠GAC；∴∠FDM +∠FMD=12∠EDG +∠GAC=12∠C+12∠BAC=12（∠BAC+∠C）=12×140°=70°；∴∠AFD=180°-（∠FDM +∠FMD）=180°-70°=110°；故答案为115°，110°；②∠AFD=90°+12∠B，理由如下：∵AG平分∠BAC，DF平分∠EDB，∴∠CAG=12∠BAC，∠FDM=12∠EDG，∵DE//AC，∴∠EDG=∠C，∠FMD=∠GAC；∴∠FDM +∠FMD=12∠EDG +∠GAC=12∠C+12∠BAC=12（∠BAC+∠C）=12×（180°-∠B）=90°-12∠B；∴∠AFD=180°-（∠FDM +∠FMD）=180°-（90°-12∠B）=90°+12∠B；（2）∠AFD=90°-12∠B，理由如下：如图，射线ED交AG于点M，∵AG平分∠BAC，DF平分∠EDB，∴∠CAG=12∠BAC，∠NDE=12∠EDB，∴∠FDM=∠NDE=12∠EDB，∵DE//AC，∴∠EDB=∠C，∠FMD=∠GAC；∴∠FDM=∠NDE=12∠C，∴∠FDM +∠FMD =12∠C+12∠BAC=12（∠BAC+∠C）=12×（180°-∠B）=90°-12∠B；∴∠AFD=∠FDM +∠FMD=90°-12∠B.【点睛】本题考查了角平分线的定义、平行线的性质、三角形的内角和定理及三角形外角的性质，根据角平分线的定义、平行线的性质、三角形的内角和定理及三角形外角的性质确定各角之间的关系是解决问题的关键.13．（1）∠AEB的大小不会发生变化，∠ACB=45°；（2）30°，60°；（3）60°或72°．【分析】（1）由直线MN与直线PQ垂直相交于O，得到∠AOB＝90°，根据三角形的外角的性质得到∠解析：（1）∠AEB的大小不会发生变化，∠ACB=45°；（2）30°，60°；（3）60°或72°．【分析】（1）由直线MN与直线PQ垂直相交于O，得到∠AOB＝90°，根据三角形的外角的性质得到∠PAB+∠ABM＝270°，根据角平分线的定义得到∠BAC＝12∠PAB，∠ABC＝12∠ABM，于是得到结论；（2）由于将△ABC沿直线AB折叠，若点C落在直线PQ上，得到∠CAB＝∠BAQ，由角平分线的定义得到∠PAC＝∠CAB，即可得到结论；根据将△ABC沿直线AB折叠，若点C落在直线MN上，得到∠ABC＝∠ABN，由于BC平分∠ABM，得到∠ABC＝∠MBC，于是得到结论；（3）由∠BAO与∠BOQ的角平分线相交于E可得出∠E与∠ABO的关系，由AE、AF分别是∠BAO和∠OAG的角平分线可知∠EAF＝90°，在△AEF中，由一个角是另一个角的32倍分情况进行分类讨论即可．【详解】解：（1）∠ACB的大小不变，∵直线MN与直线PQ垂直相交于O，∴∠AOB＝90°，∴∠OAB+∠OBA＝90°，∴∠PAB+∠ABM＝270°，∵AC、BC分别是∠BAP和∠ABM角的平分线，∴∠BAC＝12∠PAB，∠ABC＝12∠ABM，∴∠BAC+∠ABC＝12（∠PAB+∠ABM）＝135°，∴∠ACB＝45°；（2）∵将△ABC沿直线AB折叠，若点C落在直线PQ上，∴∠CAB＝∠BAQ，∵AC平分∠PAB，∴∠PAC＝∠CAB，∴∠PAC＝∠CAB＝∠BAO＝60°，∵∠AOB＝90°，∴∠ABO＝30°，∵将△ABC沿直线AB折叠，若点C落在直线MN上，∴∠ABC＝∠ABN，∵BC平分∠ABM，∴∠ABC＝∠MBC，∴∠MBC＝∠ABC＝∠ABN，∴∠ABO＝60°，故答案为：30°，60°；（3）∵AE、AF分别是∠BAO与∠GAO的平分线，∴∠EAO＝12∠BAO，∠FAO＝12∠GAO，∴∠E＝∠EOQ﹣∠EAO＝12（∠BOQ﹣∠BAO）＝12∠ABO，∵AE、AF分别是∠BAO和∠OAG的角平分线，∴∠EAF＝∠EAO+∠FAO＝12（∠BAO+∠GAO）＝90°．在△AEF中，∵∠BAO与∠BOQ的角平分线相交于E,∴∠EAO= 12∠BAO，∠EOQ=12∠BOQ，∴∠E=∠EOQ-∠EAO=12（∠BOQ-∠BAO）=12∠ABO，∵有一个角是另一个角的32倍，故有：①∠EAF＝32∠F，∠E＝30°，∠ABO＝60°；②∠F＝32∠E，∠E＝36°，∠ABO＝72°；③∠EAF＝32∠E，∠E＝60°，∠ABO＝120°（舍去）；④∠E＝32∠F，∠E＝54°，∠ABO＝108°（舍去）；∴∠ABO为60°或72°．【点睛】本题主要考查的是角平分线的性质以及三角形内角和定理的应用.解决这个问题的关键就是要能根据角平分线的性质将外角的度数与三角形的内角联系起来，然后再根据内角和定理进行求解.另外需要分类讨论的时候一定要注意分类讨论的思想．14．（1）见解析；（2）①③；（3）∠APB 的度数是10°或20°或40°或110°【分析】（1）由和是的角平分线，证明即可；（2）根据“准互余三角形”的定义逐个判断即可；（3）根据“准互余三角解析：（1）见解析；（2）①③；（3）∠APB 的度数是10°或20°或40°或110°【分析】（1）由90ABC A ∠+∠=︒和BD 是ABC 的角平分线，证明290ABD A ∠+∠=︒即可； （2）根据“准互余三角形”的定义逐个判断即可；（3）根据“准互余三角形”的定义，分类讨论：①2∠A +∠ABC =90°；②∠A +2∠APB =90°；③2∠APB +∠ABC =90°；④2∠A +∠APB =90°，由三角形内角和定理和外角的性质结合“准互余三角形”的定义，即可求出答案．【详解】（1）证明：∵在Rt ABC 中，90ACB ∠=︒，∴90ABC A ∠+∠=︒，∵BD 是ABC ∠的角平分线，∴2ABC ABD ∠=∠，∴290ABD A ∠+∠=︒，∴ABD △是“准互余三角形”；（2）①∵70,10B C ∠=︒∠=︒，∴290B C ∠+∠=︒，∴ABC 是“准互余三角形”，故①正确；②∵60A ∠=︒， 20B ∠=︒，∴210090A B ∠+∠=︒≠︒，∴ABC 不是“准互余三角形”，故②错误；③设三角形的三个内角分别为,,αβγ，且αβγ<<，∵三角形是“准互余三角形”，∴290αβ+=︒或290αβ+=︒，∴90αβ+<︒，∴180()90γαβ=︒-+>︒，∴“准互余三角形”一定是钝角三角形，故③正确；综上所述，①③正确，故答案为：①③；（3）∠APB的度数是10°或20°或40°或110°；如图①，当2∠A+∠ABC=90°时，△ABP是“准直角三角形”，∵∠ABC=50°，∴∠A=20°，∴∠APB=110°；如图②，当∠A+2∠APB=90°时，△ABP是“准直角三角形”，∵∠ABC=50°，∴∠A+∠APB=50°，∴∠APB=40°；如图③，当2∠APB+∠ABC=90°时，△ABP是“准直角三角形”，∵∠ABC=50°，∴∠APB=20°；如图④，当2∠A+∠APB=90°时，△ABP是“准直角三角形”，∵∠ABC=50°，∴∠A+∠APB=50°，所以∠A=40°，所以∠APB=10°；综上，∠APB的度数是10°或20°或40°或110°时，ABP△是“准互余三角形”．【点睛】本题是三角形综合题，考查了三角形内角和定理，三角形的外角的性质，解题关键是理解题意，根据三角形内角和定理和三角形的外角的性质，结合新定义进行求解．15．(1)50°；(2)①见解析;②见解析;(3)360°.【分析】（1）根据题意，已知，，可结合三角形内角和定理和折叠变换的性质求解； （2）①先根据折叠得：∠ADE=∠A′DE ，∠AED=∠A′解析：(1)50°；(2)①见解析;②见解析;(3)360°.【分析】（1）根据题意，已知70C ∠=︒，65B ∠=︒，可结合三角形内角和定理和折叠变换的性质求解；（2）①先根据折叠得：∠ADE=∠A′DE ，∠AED=∠A′ED ，由两个平角∠AEB 和∠ADC 得：∠1+∠2等于360°与四个折叠角的差，化简得结果；②利用两次外角定理得出结论；（3）由折叠可知∠1+∠2+∠3+∠4+∠5+∠6等于六边形的内角和减去（∠B'GF+∠B'FG ）以及（∠C'DE+∠C'ED ）和（∠A'HL+∠A'LH ），再利用三角形的内角和定理即可求解．【详解】解：（1）∵70C ∠=︒，65B ∠=︒，∴∠A′=∠A=180°-（65°+70°）=45°，∴∠A′ED +∠A′DE =180°-∠A′=135°，∴∠2=360°-（∠C+∠B+∠1+∠A′ED+∠A′DE ）=360°-310°=50°；（2）①122A ∠+∠=∠,理由如下由折叠得：∠ADE=∠A′DE ，∠AED=∠A′ED ，∵∠AEB+∠ADC=360°，∴∠1+∠2=360°-∠ADE-∠A′DE -∠AED-∠A′ED=360°-2∠ADE-2∠AED ，∴∠1+∠2=2（180°-∠ADE-∠AED ）=2∠A ；②221A ∠=∠+∠，理由如下：∵2∠是ADF 的一个外角∴2A AFD ∠=∠+∠.∵AFD ∠是A EF '△的一个外角∴1AFD A '∠=∠+∠又∵A A '∠=∠∴221A ∠=∠+∠（3）如图由题意知，∠1+∠2+∠3+∠4+∠5+∠6=720°-（∠B'GF+∠B'FG）-（∠C'DE+∠C'ED）-（∠A'HL+∠A'LH）=720°-（180°-∠B'）-（180°-C'）-（180°-A'）=180°+（∠B'+∠C'+∠A'）又∵∠B=∠B'，∠C=∠C'，∠A=∠A'，∠A+∠B+∠C=180°，∴∠1+∠2+∠3+∠4+∠5+∠6=360°．【点睛】题主要考查了折叠变换、三角形、四边形内角和定理．注意折叠前后图形全等；三角形内角和为180°；四边形内角和等于360度．。