培优专项训练八

第一篇：培优专项训练八

培优专项训练八

Unit 8 主题阅读

阅读理解

A

Zhao Hua is a student from a university.He has led a group of university student volunteers since last year.They help children at a primary school with their studies and daily lives.“ When I was a small child,” Zhao said, “ I knew March 5th was a day for people to learn from Lei Feng and help others, but I didn‟t know the real meaning of the spirit of Lei Feng.Now when I see the smiling faces of the kids I have helped, I deeply understand Lei Feng.Helping others makes me happy.”Lei Feng（1940—1962）is one of the best-known soldiers in Chinese history.He lost his parents when he was very young.His neighbors brought him up.He died in an accident at the age of 22.He did manymoney to the parents of another soldier, and bought a ticket for a woman he didn‟t know without telling her his name.On March 5th,1963, Chairman Mao called on people to “ Learn from Lei Feng” and made the day“Lei Feng Day”.Today almost 50 years has passed since Lei Feng‟s death.Some people say that the spirit of Lei Feng is out.There have been many reports about the coldness(冷漠)of people towards strangers.This has made many Chinese people think deeply about themselves.Many people think we need to promote(提倡)that spirit again.The important thing is that we must be ready to help others and make it a habit.1.Which day is “Lei Feng Day”？

A.May 3 rd.B.May 5 th.C.March 3 rd.D.March 5 th.2.Who brought Lei Feng up?

A.His parents.B.Chairman Mao.C.His neighbors.D.Soldiers.3.The underlined phrase “good deeds” means _________ in Chinese.A.好人B.好事C.好梦D.好主意

4.Which of the following is NOT TRUE according to the passage?

A.Lei Feng gave his money to another soldier‟s

parents.B.Lei Feng bought a ticket for a woman and he

told his name to her.C.Lei Feng always helped others.D.We should learn from Lei Feng.5.What‟s the best title(标题)of this passage ?A.Lei Feng‟s SpiritB.Lei Feng‟s death

C.Lei Feng‟s good neighborsD.University Student Volunteers

B

Like many people, I have no clear idea about heroes.At some point, we all wonder if we need a hero and what a hero really is.Although there are a lot of differences in cultures, heroes around the world generally share a number of characteristics(特点)which give us courage and make us want to learn from them.A hero does something worth talking about.A hero has a special story to tell and people think highly of it.But a hero is not just the person with great fame(声誉).A hero has powers(力量)larger than himself.Some people want to live like a hero, and they have to experience life with a new and further meaning.A sure test for would-be heroes is what or whom they serve.What do they want to live and die for? If the answer suggests they serve only their own fame, they may be famous persons but not heroes.the power to move people.He creates new possibilities.Without Gandhi, India might still be part of Britain.Without Martin Luther King, Jr., Americans might take different buses, eat in different restaurants, go for walks in different parks, and shop in different stores because of the different colours of their skin.There might be changes in society without a hero, but the speed of change would be rather slow.Thanks to heroes in history, they make the society develop so rapidly.1.According to this passage, a hero is a person who always ________.A.gives us courage

B.thinks highly of othersC.shares great fame

D.stands on the mountaintop

2.If you want to live like a hero, you should _______.A.experience a new and meaningful lifeB.listen to something worth talking aboutC.serve your own fame and try to be famous D.know where and how you want to live and die 3.The underlined word “vision” in the passage means “__________”.A.风景B.想象C.远见D.形象

4.Black people in America used to __________ before Martin Luther King, Jr..A.shop at the white‟s storesB.drive buses with the whiteC.take walks in the white‟s parksD.eat in restaurants without the white5.What can we learn from the passage?

A.We don‟t need heroes anymore at some point now.B.Heroes are all the same though different in cultures.C.People get powers from heroes to move to a new place.D.Our society has developed faster because of heroes in history.综合提升训练

（八）I.单项选择

1.This is ________interesting story and it is also ________ useful one.A.an;anB.an;theC.an;aD.a;a 2.I don‟t like this one.Please show me ________ one.A.otherC.anotherA.Germen

B.the othersD.the other oneB.Germany

D.Germans

3.There are five ________over there.C.Germanys

4.I think you can do the work ________.A.yourselfB.myselfC.himselfD.your 5.The ________of the planes made us feel sick.A.voiceB.noiseC.soundD.smell 6.________ good health you have!

A.How aB.What aC.HowD.What

7.This plane is made ________ paper and it was made ________ my mother last night.A.of;byB.from;byC.with;forD.in;with

8.They all looked ________at the teacher and felt very ________.A.happy;happyC.happy;happily A.many

B.happily;happilyD.happily;happy C.littleD.a lot of

9.It was a dry year.We‟ve had ________ rain.B.a few

10.Could you tell me when the meeting ________? A.beginB.beginsC.will beginD.beginning

11.I don‟t know the school, but it‟s ________ to be quite a good one.A.told B.spokenC.talkedD.said A.is finished

B.was finished

12.When your homework ________, you may go home.C.will be finishedD.has finished

13.When I looked into the room, I found Philip himself ________ in bed.A.lies

B.lyingC.lay

D.lie

14.The Wangs ________here for ten years.A.is livingB.have livedC.has livedD.lives

15.They ________the station ________the train started.A.won‟t leave;until

B.not leave;untilD.left;until

C.didn‟t leave;until II．完形填空

Ever since I was little, my favourite season was winter.I loved to play in the snow and enjoyed the hot chocolate.winter never gave me the special gift of snow on my birthday.I would ask my it didn‟t snow on my birthday.She would laugh and tell me I asked too many questions.one day, she promised that she would make it snow on my next

birthday.That year, my birthday, my grandmother died.I was sad but angry because she had promised to make it snow.The day of my sixth birthday, I woke up and ran to the window, hoping to see just one snowflake(雪花).But there was no.I felt mad at my grandmother.She had broken a promise.By my sixteenth birthday, I , even though I still wished for it.During my party, I stayed with my friends and family and was truly Then I saw the white snow down all around.I was so excited that I ran around screaming and laughing.My friends all laughed me, but I didn‟t care.When I home, my grandpa said he had a gift for me.I was given me a gift.It was a small white box, which looked old.I opened it.There was a crystal snowflake(冰晶雪花)with a card that , “Happy Birthday.”

How could this be? My grandpa said it was my grandmother‟s final on my “sweet I was that my smiling grandmother angel was and had been watching over me.B.Unluckily

sixteenth”.I cried.16.A.Certainly

C.ImportantlyD.Luckily

17.A.whenB.howC.whetherD.why 18.A.ButB.OrC.Then19.A.onB.afterC.before21.A.had gotC.had found

D.So D.in

20.A.seasonB.snowC.breakfastD.winter

B.had madeD.had lost

D.feared

22.A.happyB.sadC.angryD.sorry 23.A.hadB.wasC.played24.A.fell

C.disappearingD.falling25.A.withB.atC.from

D.off

D.flew

26.A.arrived atB.reached atC.got

B.standing

27.A.excitedB.surprisedC.pleasedD.sad 28.A.wroteB.saidC.explainedD.appeared 29.A.orderB.mistakeC.wishD.decision 30.A.sureB.angryC.sadD.confident III.阅读理解

Mrs.Blanches‟ husband went off on a business trip to America.He planned to leave New York for Washington.He wanted to catch the 4:00 pm plane to Washington.It was seven o‟clock in the afternoon.Mrs.Blanches received a telephone call from her husband.He told her that he was still at the New York airport.Mrs.Blanches was so surprised and asked him what happened.“What happened, honey?” asked Mrs.Blanches.“Well,” said Mr.Blanches.“I really don‟t know what happened, honey.Everything was going fine.At half past three, I got my air ticket, checked my luggage and waited in line at the gate.I walked across the runaway(飞机跑道)to the airport and on my way I saw one of my old friends.Have you

remembered him? His name is Jack Smith.Now Jack Smith is an engineer who works at the airport.I was excited that I shouted to him.I came up and wanted to shake hands with Jack.But a policeman ran to me quickly and caught me.”

“Why did he catch you?” Mrs.Blanches asked.“I don‟t know,” said Mr.Blanches.All I said was“Hi,Jack!”

“Yeah, that is why they wouldn‟t let you go,” said Mrs.Blanches.“They thought you were going to do harm to the whole plane.Only terrorists want to take control of a plane, and that is called „

31.What was Mrs.Blanches‟ husband‟s destination(目的地)? A.Washington, America.B.South America.C.New York.D.The New York airport.32.Where was Mr.Blanches when he called his wife? A.He was on the airport to Washington.B.He was still at the New York Airport.C.He was in Washington.D.He was on the railway station.33.Who was Jack Smith?

A.Mr.Blanches‟ new customer.B.Mr.Blanches‟ old customer.C.Mr.Blanches‟ brother.D.Mr.Blanches‟ friend.34.What does the underlined word mean in Chinese？

A.恐怖B.逮捕C.劫机 D.别动

35.Why did the policeman catch Mrs.Blanches‟ husband?

A.Because they thought he was going to do harm to the plane.B.Because they wanted to get his help in catching terrorists.C.Because they knew that he was a terrorist.D.Because Mrs.Blanches asked them to do so.IV．词汇运用

36.Please help _______(你自己)to some fish, Tom.Don‟t be so shy.37.Man can‟t live ________(没有)water, so we must make good use of it.38.Please listen to the speaker _________(仔细地)when he speaks.39.She is such a pleasant and _________(有帮助的)girl that we all like her.40.The foreign teachers in our school are from Germany.They are ________(德国人).V.句型转换

对画线部分 提问)

_________ _________ does a football match last?

42.The old lady was so tired that she couldn‟t go any further.(改为简单句)

The old lady was _________ _________ to go any further.43.Their new house is twice as big as the old one.(改为同义句)

Their new house is twice _______ ________of the old one.44.I wonder how I can get to the nearest underground station.（改为同义句）I wonder ________ _______get to the nearest underground station.45.If you do exercise a lot, you will be healthy.（改为同义句）

The ______ exercise you do, the _______ you will be.

第二篇：2013届高三英语词汇专项训练(八)

2013届高三英语词汇专项训练

（八）一、用所给单词的适当形式完成句子

1.His inability to speak to English put him at a _________(advantage)at the international conference.2.Do you know anymore with a mental or physical _________(disabled)?

3.On Christmas Eve, we helped to put up the Christmas tree, the _______(decorate)and the balloons.4.With the __________(develop)of modern agriculture and industry, more waste has been produced.5.The coat is so ______(dirt)that I’ll take it to the cleaner’s.二、根据首字母或中文提示完成句子

1.The next day, Us President Franklin Roosevelt d_________ war against Japan.2.They worked from d__________ till dusk to meet the deadline.3.To what d__________ is he interested in playing computer games? 4.He turned a d__________ ear to our advice and now he is trouble.5.How excited they were!They d________ Class 5 in the football match and won the game yesterday.6.As usual, let’s have a __________(听写)of some English words and expressions.7.I’m terribly sorry, but didn’t do that ___________(故意地)

8.On our ___________(启程，离开)from Tahiti, some of the crew took over the ship.9.The beauty of Guilin is beyond ____________(描述)

10.It’s hard to imagine how this quiet volcano _________(毁灭)the whole city.三、改写同一句，每空一词

1.The temple we visited last week has a history of thousands of years.The history of the temple that we visited last week can ____ _____ _____ thousands of years ago.2.When we are attacked, all of us will take up arms and fight to defend our country.When ________, all of us will take up arms and fight _______ _______ ________ country.3.My aunt Mary delivered a healthy and lovely girl this morning.My aunt Mary ____ _____ _____ a healthy and lovely girl this morning.4.The future of space research is dependent on how much money we have..The future of space research _______ _______ how much money we have.5.I’m sad that I can’t adapt to the climate here._____ _____ ______ , the climate here __________ ___________ me.四、选词填空

1.They worked _______(deep, deeply)into the night, by which we are ______(deep, deeply)moved.2._______(Some day, The other day)I met him in the street and he told me that he would come to see me _______(some day, the other day).3.The police accused him of setting fire to the building but he _________(deny, refuse)having been in the area in the night of fire.五、选择填空

1.The snake hasn’t bitten me yet, but I daren’t _____ to upset it.A.to do a thingB.do anythingC.to do somethingD.do nothing 2.____ the advances of science, the discomforts of the old age will no doubt always be with us.A.As forB.BesidesC.ExceptD.Despite 3.The policemen went into action _______ they heard the alarm.A.swiftlyB.presentlyC.quicklyD.directly 4.I saw the train leaving ______ the direction of Shanghai.A.in

B.to

C.withD.at 5.I can see a light _____ the distance, and I also see a strange _________ a distance of ten yards.A.in, inB.in, atC.at, inD.at, at 6.Her son, to whom she was so ________, went abroad for further education two years ago.A.loved

B.cared

C.devoted

D.affected 7.Over the past decades, sea ice ___ in the Arctic as a result of global warming.A.had decreasedB.decreasedC.has been decreasingD.is decreasing 8.The way he did it was different ________ we were used to.A.in whichB.in whatC.from whatD.from which 9.One of the best ways for people to keep fit is to ______ healthy eating habits.A.grow

B.develop

C.increase

D.raise六、一句多译

1.我的外套和你的外套在颜色和款式方面不同，但尺码相同

1)_________________________________________________________________2)_________________________________________________________________ 2.你能辨别金星（Venus）和其它的行星吗？

1)_________________________________________________________________2)_________________________________________________________________ 3.令我非常高兴的是，我通过了考试，拿到了驾照

1)_________________________________________________________________ 2)_________________________________________________________________ 4.我们发现他是个很难相处的人。

1)_________________________________________________________________2)_________________________________________________________________ 5.听到考试没及格的坏消息，他感到非常失望。

1)_________________________________________________________________2)_________________________________________________________________

第三篇：基础知识训练 八

基础知识训练 八

1、下列词语中加点字的读音完全正确的一组是（）

A．坯子（pī）稂莠（láng）装模作样（mú）少安毋躁（shāo）B．经幢（chuáng）标识（shí）扛鼎之作（gāng）拾级而上（shè）

C．褊狭（biǎn）掂量（liáng）呼天抢地（qiāng）疾风劲草（jìng）D．答应（dá）供职（gòng）强词夺理（qiǎng）不着边际（zhuó）

2、下列词语中没有错别字的一组是（）A．辨证揣摩暮鼓晨钟格物致知B．禀承 噩梦无事生非固步自封C．含盖担搁浮想联篇若即若离D．告罄撤消顾名思义兵慌马乱

3、依次填入下列各句横线的词语，最恰当的一组是（）

[1]因为还有别的事，经理不得不提前离去，他离开前一再我们要处理这起商品质量纠纷，一定要给消费者一个满意的答复。

[2]由于交通事业的迅速发展，为城乡物资交流提供了更为有利的条件。[3]这仅是你个人的观点，而且论据不充分，不能别人接受。A．交待从而强制B．交代从而强迫C．交待进而强制D．交代进而强迫

4、下列各句中加点的成语使用恰当的一句是（）A．病菌虽说是微不足道的，但它对人的危害却是非常严重的。

B．为了写这篇文章，刘教授查找文献，寻章摘句，做了上千张卡片，费了很多时间和精力C．人非圣贤，孰能无过？犯点小错误是在所难免的，也是不足为训的，关键是要吸取教训。D．金三角的贩毒分子，在从境外获得轻武器补充后，如虎添翼，制毒更加猖狂。

5、下列各句中没有语病的一句是（）

A．经调查，刘晓庆及其所办的两个有限公司自1996年以来，采取不列、少列收入，多利支出，虚假申报，通知申报而拒不申报，偷逃税款1458.3万元。

B．在滴水成冰的冬季，筑路大军冒着料峭的北风在工地上紧张地劳动着。

C．使用300电话卡不需要专用的电话机，如果能牢记自己的卡号和密码您可以不必随身携带300卡，因此它比磁卡和IC卡更加方便。

D．桐城派之所以“别树一宗”并非由于清代文化政策或传统势力的支持影响，更重要的是因为它的理论的合理性。

6．下列各句中标点符号使用正确的一项是（）

A．这件事是让你去做好呢？还是让我去做好呢？B．你要不断进步、识字、生产

C．张华考上北京大学，在化学系学习；李萍进了中等技术学校，读机械制造专业；我在百货公司当售货员：我们都有光明的前途。

D．现代画家徐悲鸿笔下的马，正如有的评论家说的那样，“形种兼备，充满生机。”

基础知识训练 九

1、下列词语中加点的字的读音完全不相同的一组是（）A．甲醛蜷曲诠释得鱼忘筌权宜之计B．泥淖拙笨灼灼卓尔不群擢发难数C．懒怠瘌痢水獭春意阑珊天籁之音D．庇护秕谷臂膀筚路蓝缕笔墨官司

2、下列句子中没有错别字的一句是（）

A．我们不能墨守成规，而要坚持科学研究先行，及时开发新的美容化装产品。

B．至少有如下两点足可令人三思：第一，文学创作和市场运作并非水火不相融；第二；文学创作绝对不是简单的市场运作。

C．翻开书卷，构想那美丽的画面，放纵自己的心随主人公起起伏伏，想像主人公的音容笑貌，或远隔时空与作者对话，咀嚼文字中的言外之意，弦外之音，这是一种何等的享受！D．他劝告那些不愿为公平竞争开绿灯的医药批发企业，如果还抱残守缺，只会“为渊驱鱼，为丛驱鹊”，最终将失去市场，无法生存。

3、依次填入下列各句横线处的词语，最恰当的一组是（）

[1]专家提醒消费者，购买商品房一定要注意，对于“”依据《合同法》相关规定，双方有约定的按照约定执行；如果无约定，经营者违约时应双倍返还，消费者违约时不予返还。[2]既然称作“中学生新概念作文选”，就要编得中学生阅读。

[3]来自中国银监会的信息显示，四大银行的上市时间表基本排定，并以先海外、后国内的顺序进行。

A．定金合适大概B．订金合适大致C．定金适合大致D．订金适合大概4下列各句中加点的成语使用恰当的一句是（）

A．一开盘，这只股票就一路狂跌，势如破竹，使已经遭受股市重重打击的股民又雪上加霜。B．我，15岁，一个中学三年级学生，在读了许多报刊文学之后，心血来潮，见猎心喜，也学写了一篇小说，冒失的向文学刊物投稿。

C．作者的这些散文，曾有十多篇在本报刊载过，因为受到许多读者的喜爱，作者才连篇累牍地写下去。

D．董事长，对您的好意，我只能敬谢不敏，因为我有自知之明，我做些具体的工作尚可，经理一职实难胜任。

5、下列各句中没有语病的一句是（）

A．从古老的刀耕火种，到21世纪的现代化农副产品基地，悠长的岁月，教会了勤劳的松江人怎样生活在这片土地上。

B．据了解，我市移动电话部门针对春节期间手机短信密集发送，对今年发送量进行了预测，并事先做好相关准备工作。

C．时下的店名和商品名在吸收外来词时，追求时髦，哗众取宠，令人费解。这些叫人看不懂的名称，只能让人贻笑大方。

D．美国宇航局引以为豪的“勇气”号火星车21日清晨突然发生故障，之后连续30小时不再向地面传回任何有效信息，所有参与此项目的科学家全都各就各位昼夜不停地寻找解决故障的对策。

6、填入下列横线处与上文衔接最恰当的一项是（）

这就是汉字，我的祖屋，我的家！我迷恋它雕梁画栋的亭阁楼台，我更迷恋它朝晖夕阴中隶楷行草的万千气象：

[1]赏心悦目的，是耀眼的光箭穿过宽阔而幽深的甬道，照亮祖屋的身躯，优雅而颀长；[2]心驰神曳的，是光线将祖屋分明的棱角隐去，只留轻盈身姿，飘飘欲飞；[3]令人陶醉的，是道道金辉，铺撒祖屋的胸襟，舒展高贵，气度雍容；[4]最最摄魂夺魄的，当是斑驳的树影中，祖屋如龙蛇行走，曼妙莫测！

A．[1][2][3][4]B．[1][3][2]C．[2][4][1][3]D．[1][4][2][3]

第四篇：全等三角形培优专题训练

做最适合你的数学培训

八年级数学培优专题训练

（二）探索三角形全等的条件

1、一张长方形纸片沿对角线剪开，得到两张三角形纸片，再将这两张纸片摆成如下图形式，使点B、F、C、D

CA在同一条直线上.EAEP MN⑴求证：AB⊥ED；

⑵若PB＝BC，请找出图中与此条件有关的一对全等三角形，并给予证明

2、如图，在△ABC中，AC＝BC，∠ACB＝90°，AD平分∠BAC，BE⊥AD交AC的延长线于F，E为垂足，则结论：①AD＝BF；②CF＝CD；③AC＋CD＝AB；④BE＝CF；⑤BF＝2BE.其中正确的是（）

3、如图，点C在线段AB上，DA ⊥AB，EB⊥AB，FC⊥AB，且DA＝BC，EB＝AC，FC＝AB，∠AFB＝51°，求∠DFC的度数.DFFBDBFCDBEDCAE

ACBF________________________________________________________________________________________________________________

周老师·数学培优

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4、如图，四边形ABCD中，AB∥CD，AD∥BC，O为对角线AC的中点，过点O作一条直线分别与AB、CD交于点M、N，点E、F在直线M、N上，且OE＝OF.⑴图中共有几对全等三角形，请把它们都写下来； ⑵求证：∠MAE＝∠NCF

AEBMONCDF5、在△ABC中，高所在直线AD和BE交于H点，且BH＝AC，则∠ABC＝_____________.6、下列三个判断：

⑴有两边及其中一边上的高对应相等的两个三角形全等； ⑵有两边及第三边上的高对应相等的两个三角形全等； ⑶一边及其它两边上的高对应相等的两个三角形全等.上述判断是否正确？若正确，说明理由；若不正确，请举出反例.________________________________________________________________________________________________________________

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（三）全等三角形的应用

全等三角形常用来转移线段和角，用它来证明：

①线段和角的等量关系 ②线段和角的和差倍分关系

③直线与直线的平行或垂直等位置关系

1、如图，已知BD、CE分别是△ABC的边AC和AB上的高，点P在BD的延长线上，BP＝AC，点Q在CE上，CQ＝AB.试判断AP与AQ的关系，并证明.2、如图，AD是△ABC的高，E为AC上一点，BE交AD于点F，且BF＝AC，FD＝CD，求证：BE⊥AC

FAADQPEBCE3、（2012〃阜新中考）如图,在△ABC中,AB＝AC,AD＝AE,∠BAC＝∠DAC＝90°.⑴当点D在AC上时,如图①,线段BD,CE有怎样的数量和位置关系?证明你猜想的结论.⑵将图①中的△ADE绕点A顺时针旋转α角(0°＜α＜90°)，如图②，线段BD、CE有怎样的数量关系和位置关系？问明理由.BEABDCDC①AEDBC②________________________________________________________________________________________________________________

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4、在△ABC中，AB＝AC，点D是直线 BC上一点（不与B、C重合），以AD为一边在AD的右侧作△ADE，使AD＝AE，∠DAE＝∠BAC，连接CE.⑴如图①，当点D在线段BC上时，若∠BAC＝90°，则∠BCE＝_______度.⑵设∠BAC＝α，∠BCE＝β

a、如图②，当点D在线段BC上移动时，α，β之间有怎样的数量关系？请说明理由.b、当点D在直线BC上移动时，α，β之间有怎样的数量关系？请直接写出你的结论.BDAEBDC①AEC②________________________________________________________________________________________________________________

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（四）辅助线作法之连接法

在几何证明中，常通过添加辅助线来构造全等三角形.常见的添加辅助线方法有：连接法、截长补短法、倍长中线法、翻折法、旋转法以及利用特殊条件构造全等三角形等等.1、如图，△ABC的两条高BD，CE相交于点P，且PD＝PE.证明∶AC＝AB

2、已知AB＝DE，BC＝EF，∠B＝∠E，AF＝CD 求证：AC∥DF

3、如图，AB交CD于点O，AD、CB的延长线相交于点E，且OA＝OC，EA＝EC.∠A＝∠C吗？点O在∠AEC的平分线上吗？

EBCDOABCDAFEAEBDPC________________________________________________________________________________________________________________

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（五）辅助线作法之倍长中线法

在题目条件中含有中线的问题，我们常用的辅助线就是将中线延长一倍，其目的是为了得一对全等三角形，将分散的条件集中到一个三角形中去.1、△ABC中，AB＝5，AC＝3，求中线AD的取值范围.2、如图，在△ABC中，AD是∠BAC的平分线，又是BC上的中线

求证：AB＝AC

3、（2014〃襄阳初三模拟）在△ABC中，D是边BC上的一点，且CD＝AB，∠BAD＝∠BDA，AE是△ABD的中线.求证∶AC＝2AE

BEDCABDCAABDC________________________________________________________________________________________________________________

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AFE4、（竞赛014）△ABC中，D为BC的中点，DE⊥DF交AB，AC于点E，F.求证：BE＋CF＞EF

6、（竞赛015）例：已知AD是△ABC的中线，BE交AC于点E，交AD于点F，且AE＝EF.求证:AC＝BF

BDCAEFDBC________________________________________________________________________________________________________________

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（六）辅助线作法之截长补短法

截长法：在第三条线段上截下一段使其等于两条线段中的一条，再证明剩余部分与另一条相等.补短法：把两条线段中的一条补到另一条线段上去，证明所得新线段与第三条线段相等.1、已知AC∥BD，EA，EB分别平分∠CAB和∠DBA，点E在CD上.求证：AB＝AC＋BD

2、在四边形ABCD中，AC平分∠BAD，CE⊥AB于点E，且AE＝½（AB＋AD）.求证∶∠B＋∠D＝180°

3、如图，已知△ABC中，∠A＝90°，AB＝AC，D为AC的中点，AE⊥BD于E，延长AE交BC于F.求证：∠ADB＝∠CDF

________________________________________________________________________________________________________________

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4、如图，∠C＝90°，AC＝BC，AD是∠BAC的角平分线.求证∶AC＋CD＝AB

12、如图，已知AB＝CD＝AE＝BC＋DE＝2，∠ABC＝∠AED＝90°，求五边形ABCDE的面积.CBABDCDAE________________________________________________________________________________________________________________

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（七）辅助线作法之利用特殊条件构造全等三角形

2、（2012〃“华罗庚杯”）如图，在△ABC中，AC＝½AB，AD平分∠BAC，且AD＝BD 求证：CD⊥AC

ACBD________________________________________________________________________________________________________________

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（八）全等三角形在动态几何中的运用

1、(竞赛〃014〃3)如图，△ABC的边BC在直线l上，AC⊥BC，且AC＝BC.△EFP的边FP也在直线l上，边EF与边AC重合，且EF＝FP.⑴在图①中,请你通过观察、测量、猜想并写出AB与AP所满足的数量关系和位置关系;⑵将△EFP沿直线l向左平移到图②的位置时,EP交AC于点Q,连接AP,BQ.猜想并写出BQ与AP所满足的数量关系和位置关系,并证明你的猜想;⑶将△EFP沿直线l向左平移到图③的位置时,EP的延长线交AC的延长线于点Q,连接AP,BQ.你认为⑵中所猜想的BQ与AP的数量关系和位置关系还成立吗?若成立,给出证明;若不成立,请说明理由.A(E)EAEAQllBC(F)PFPBClBFCP Q________________________________________________________________________________________________________________

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（九）探究角平分线

一、知识清单

角平分线的定义：从一个角的顶点引出一条射线，把这个角分成两个相等的角，这条射线叫做这个角的角平分线.三角形的角平分线定义：三角形的一个角的平分线与这个角的对边相交，连结这个角的顶点和与对边交点的线段叫做三角形的角平分线（也叫三角形的内角平分线）.由定义可知，三角形的角平分线是一条线段.角平分线性质:

1、角平分线上的点，到这个角的两边的距离相等.2、角平分线分得的两个角相等，都等于该角的一半.3、三角形的三条角平分线交于一点，且到各边的距离相等，这个点称为内心.二、方法点拨

证明角平分线有两种方法:一是运用定义证明两个角相等;二是运用角平分线的判定方法.三、规律清单

①遇到角平分线,可从角平分线上的某一点向角的两边作垂线段(图1).②遇到角平分线,常可利用翻折法或截长补短法解题(图2).③有两条角平分线(内角或外角)交于一点,则连接该点与三角形第三个顶点的线段会平分一个内角或外角(图3).④有垂直于角平分线的线段,则延长这条线段以利用三线合一解题(图4).⑤遇到角内的一点到角的两边有垂线段时,就连接这点与角的顶点,看能否平分已知角(图5).⑥遇到有多条角平分线时,可尝试用整体的思想解题(图6).⑦有翻折条件时,除注意全等的结论,还应关注折线就是角平分线、是对称轴（如图7）.⑧角平分线、平行线、等腰三角形三个条件中出现任意两个,常可直接得到另一个(如图8）.AAACBDAFAEGDBDBC图2B图1CD图3DCBC________________________________________________________________________________________________________________

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AA

CFEBDC图4BFE

DECF图5

ADBA1D2B3A1APFC'D'DAD2CB图6EF1＋2＋3＝90°1＋2＝90°－½BCBEC图7B图8CD

四、真题训练

1、(2011〃鄂州〃竞赛〃018 〃重庆中考）如图，△ABC的外角∠ACD的平分线CP与内角∠ABC的平分线BP相交于点P，若∠BPC＝40°，则∠CAP＝_____________.BCDAP2、(竞赛〃019)如图，∠B＝∠C＝90°，M是BC的中点，DM平分∠ADC.求证:AM平分∠DAB

DCMAB________________________________________________________________________________________________________________

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3、(竞赛〃019)如图,在△ABC中,∠BAC＝90°,AB＝AC,BE平分∠ABC,CE⊥BE.AED1求证:CE＝ BD 2

BCA

4、如图，在△ABC中，AD平分∠BAC，BD＝CD 求证：∠B＝∠C

5、如图，在Rt△ABC中，∠C＝90°，AC＝BC，AD是∠BAC的平分线，交BC于D，DE⊥AB于E，若AB＝10cm，则△DBE的周长是多少？

ABDCAECDB6、（2011，恩施中考）AD是△ABC的角平分线，DF⊥AB，垂足为F，DE＝DG，△ADG和△AED的面积分别为50和39，则△EDF的面积为多少？

BEFGDC________________________________________________________________________________________________________________

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7、如图，△ABC中，AD平分∠BAC，DG⊥BC且平分BC，DE⊥AB于E，DF⊥AC于F.求证：BE＝CF

8、在△ABC中，AD是∠BAC的平分线，E、F分别为AB、AC上的点，且∠EDF＋∠BAF＝180°

⑴求证：DE＝DF ⑵如果把最后一个条件改为AE＞AF，且∠AED＋∠AFD＝180°，那么结论还成立吗？

9、如图，已知AB＝AC，BE⊥AC于E，CF⊥AB于F，BE与CF交于点D 求证：点D在∠BAC的平分线上.10、如图，在四边形ABCD中，对角线AC平分∠BAD，AB＞AD，下列结论正确的是()A.AB－AD＞CB－CD B.AB－AD＝CB－CD C.AB－AD＜CB－CD D.AB－CD与CB－CD的大小关系不确定

BCAAEBGCFDAFEBDCBFDAECD________________________________________________________________________________________________________________

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11、（竞赛014）如图，已知△ABC中，∠B＝60°，∠BAC，∠BCA的平分线AD，CE相交于点O.求证：DC＋AE＝AC

12、(竞赛〃019)如图，已知△ABC，P为内角平分线AD、BE、CF的交点，过点P作PG⊥BC于G点。试说明∠BPD与∠CPG的大小关系，并说明理由。

BDGCAAEOBDCFPE________________________________________________________________________________________________________________

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（十）应用线段垂直平分线的性质和判定解题

一、知识清单

定义：经过线段中点并且垂直于这条线段的直线，叫做这条线段的垂直平分线。线段垂直平分线的性质：线段垂直平分线上的点与这条线段两个端点的距离相等。线段垂直平分的判定：与一条线段两个端点距离相等的点，在这条线段的垂直平分线上。

________________________________________________________________________________________________________________

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第五篇：培优班材料,平行四边形专题训练

特殊四边形专题三：特殊四边形中的探究问题

有关特殊四边形中的探究问题是涉及特殊四边形的几何动态问题，要求学生自主探索、发现问题、总结规律，因此要求同学们对一些特殊四边形的性质要掌握到位。解决此类问题的方法是先明确在变化过程中什么“不变”，特殊位置在什么地方，再从特殊到一般进行探究，这种方法在以后的数学学习中会经常用到。

【例1】已知：正方形ABCD中，∠MAN=45°，∠MAN绕点A顺时针旋转，它的两边分别交CB，DC（或它们的延长线）于点M，N，当∠MAN绕点A旋转到BM=DN时（如图1），易证MB+DN=MN。

（1）当∠MAN绕点A旋转到BM≠DN时（如图2），线段BM，DN和MN之间有怎样的数量关系？写出猜想，并加以证明；

（2）当∠MAN绕点A旋转到如图3所示的位置时，线段BM，DN和MN之间又有怎样的数量关系？写出你的猜想，并说明理由。

【例2】（1）操作发现：如图1，在矩形ABCD中，E是BC的中点，将ABE沿AE折叠后得到AFE，点F在矩形ABCD内部，延长AF交CD于点G，猜想线段GF与GC有数量关系，并证明你的结论。

（2）类比探究，如图2，将（1）中 的矩形ABCD改为平行四边形，其他条件不变，（1）中的结论是否仍然成立？并说明理由。

【例3】如图，正方形ABCD的角线AC，BD相交于点O。

（1）若E为AC上一点，过A作AGEB于G，AG，BD交于F，求证：OE=OF；

（2）若点E在AC的延长线上（如图2），AGEB交EB的延长线于G，AG的延长线交直线BD于点F，其他条件不变，OE=OF还成立吗？若成立，请给予证明；若不成立，请说明理由。