黑龍江省哈爾濱市2022年中考英語(yǔ)真題

1、2022年黑龍江省哈爾濱市初中學(xué)業(yè)水平考試英語(yǔ)試題第卷一、單項(xiàng)選擇（本題共20分，每小題1分）選擇最佳答案( )l.In the following words. which underlinedC下劃線(xiàn)的）letters have a different sound from theOthers?A.birth B.either C.earth( ) 2.Which pair of the words with the underlined letters has the same sound？A.hand camp B.drive thin C.loud double( )3.Which

2、ofthe following words doesnt have the same stress（重音）as the others？A. Behind. B.Modern. C.Photo.( )4.-What do you want to do this weekend？-Iwant to care for animals in_ animal centerA.an B.a C./( )5.- _have you been in Beijing?-For two weeks.AndI went to the Great WallA.How soon B. How long C. How o

3、fen( )6.-There will be _tomorrow.We cant eat out-Well， we have to stay at homeA.rainy B.rain C.raining( )7.-I need _ school things-Me,too. Lets go shopping.A.no B.some C.any( )8.- China held the Olympics in 2008 and 2022 successfully-We take _ in our great country.A. advice B. price C. pride( )9.-Ma

4、ny of us _our parents too much-Yes. Wed better learn to look afer ourselvesA.depend on B.put on C.get on( )10. Harbin is famous_ ice and snow. Its well worth visiting in winterA.as B.for C.to( )ll.WangYaping,the female（女性的）Chinese space walker, _her first space walk inNovember.2021A.has begun B.begi

5、ns C.began( )12.-Do you like poems?-Yes.I _read poems when I was 5.A.mustB.canC.could( )13.-I often watch talk shows on TV-I enjoy watching the news. I hope _whats going on around the worldA.find outB.to find outC.finding out( )14.-What do you do to keep healthy？-I do more sports and eat _fast food.

6、A.less B.fewer C.more( )15.-How exciting the speech is!-Pretty good! This is the best speech_ Ive ever heard.A. which B.that C.who( )16.-Could you tell me_ on weekdays?Iusually go to school on foot but sometimes by bike.A. why do you go to schoolB. when you went to schoolC. how you go to school( )17

7、.-Happiness is about having each winy wish come true-_we work hard. well make our life full of happinessA.If B.Unless C.Though( )18.The _ is Chinas national treasure.Its a kind of cute animal that likes cating bambooA.panda B.tiger C.clephant( )19. To keep safe in coming summer vacation you are supp

8、osed to refuse to let strangers inturn off the gas(煤氣）after cookinggo swimming alone in the rivertake care of your own things when you travelleak（泄露）your personal information on the IntemetA.B.C.( ) 20. Here is a survey about how to be a good learner among 400 students.According to the formBelow, _s

9、tudents have chosen “Learn from mistakes” as their key words.Key wordsMaking plans Taking notes Asking questions Learning from mistakesPercentage(百分比)20%10%30%?二、完形填空（本題共10分，每小題1分）At the age of seven.I started school in London. There I met a_21_，Mr.King.Hcinfluenced my whole life. Mr King taught me

10、maths. He was humorous. Sometimes， he told usfunny stories. So his lessons made us_22_One dayMr.King stopped me_23_lwas on my way home. He took out a piece of paperwith some maths exercises on it._24_a smile， he asked.“Would you like to have a try mykid？” I was a hit surprised and took _25_exercises

11、 home.I worked hard that nightThe next day when I gave part of the answers to him he _26_ checked them and said“Well done! l I believe your love for maths will help you with the rest.”After Mr. King encouraged me,I _27_ all my free time on the exercises. A week later. Isucceededl Mr.King gave more e

12、xercises to me,_28_me to make great progress Every time_29_ the problems,I have a lot of fun. Exercises became harder and I put effort (努力）intomaths.I enjoyed maths. It was Mr. King that opened theomaths for me and led mein，thankful to Mr. King.根據(jù)短文內(nèi)容選擇最佳答案。( )21.A.worker B.visitor C.teacher( )22.A.

13、bored B. Interested C. sleepy( )23.A.while B.until C.afer( )24.A.For B.With C.About( )25.A.this B. those C.that( )26.A.carefully B.hardly C.angrily( )27.A.cost B.paid C. spent( )28.A.expect B.to expect C. expecting( )29.A.gave out B. worked out C.ran out( ) 30.A.door B.box C.sofa閱讀理解（本題共20分，每小題1分）(A

14、)The World for Teenagers（青少年）LearningFeelingsCommunicationCommunityActivities Question in June:What do you ofen do after class？Linda from BritainIoften use old clothes that people dont wear any more to make bags.I opened a small shop inmy community and set up a website to sell the bags online.Many c

15、ustomers think they arefantastic.NowI plan to write a new ways to use old clothes.Linlin from ChinaMuseums often teach me a lotIhave ever been to many museums. such as the ones in HarbinXian and s0 on But the Hangzhou National Tea Museum is my favorite.Its in this museum that Iknew about the history

16、 of tea I watched the tea art performances （表演）. They showed how tomake a perfect cup oftea with tea sets.Amy from CanadaI often cook Chinese food at home.My favorite is Yunnan Rice Noodles.To make the food.weneed to have rice noodles,chicken soup,chicken vegetables and eggs . My parents often cookC

17、hinese food as well ,especially gongbao chicken.根據(jù)語(yǔ)言材料內(nèi)容選擇最佳答案。( )31.Teenagers from_ countries answer the questionsA. threeB.twoC.one( )32.According to the passage Linda often_A. makes Yunnan Rice NoodlesB. uses old clothes to make bagsC.visits museums( )33.You can ask Linli about _if you are intere

18、sted in tea.A. the history oftea B.the skill ofmaking tea sets C.the museum in Harbin( ) 34.Which ofthe following is TRUE according to the passage?A. Lindas bags can satisfy many customersB. Only Amys parents ofien cook Chinese foodC. Linlin learns nothing from the museums( ) 35.From the passage abo

19、ve you can find that all these teenagers often_A.share the housework at homeB.put old things to good useC.have after-class activities（B） Long long time ago,a man called Tom got a book.It was about the secret ora special pebble（鵝卵石） that could turn anything into real gold. The special pebble was lyin

20、g among other oneson the beach. Because they looked the same the special pebble was almost impossible to be foundIf people touched the special pebbleit would feel warm However other pebbles were cold. After learning the secret Tom was excited. He dreamed of becoming rich. So he told all thathe hadbo

21、ught garden forksg up pebbles. On the first day he picked up pebbles and then he threw them into the sea if there were not special. Again and againthe special pebble didn t appear But he didn t give up and then he continued. Several years later suddenly he picked up one pebble which was warm. But be

22、cause he hadsuch a strong habit of throwing one pebble afer another without thinking he threw this specialone into the sea as usual. He lost the chance to be rich. What a pity In fact good chances do come in our life at any time. Try to hold them as soon as possibleinstead of missing them根據(jù)短文內(nèi)容判斷正（A

23、）誤（B）。( )36. The special pebble that could turn anything into real gold would feel cold( ) 37. To become rich. Tom sold all that he had. went to the beach with garden forks and startedpicking up pebbles.( )38. If the pebbles were not special.Tom threw them into the sea on the first day( )39.After se

24、veral years.Tom hada strong habit of throwing books without thinking( )40.In the end.Tom found the special pebble but he missed it（C） At the beginning of human history. people could only eat food they found. But then peoplelearned to find more ways to get food. About 10. 000 years ago people slarted

25、 to farm the landAfter that，people developed farming skills People eat different food in different areasIn China rice is the main food for people in thesouth while the people in the north eat noodlesPcople who live in European countries near thesea eat lots of fish. But in Central Europe. people afe

26、away from the sea. So they dont eat SOmuch fish They eat more special meat instead. People eat food with different tools in different areas. In China, people always like useing chopsticks while in North American. Australia and Europe, people alwayslike useing knives and forks .to our surprise, in in

27、dia and the Middle East, people always pick up food with their own fingers. Now people can cat different food from different areas. As we can see it is possible toconvey food casily from one part of the world to another. We can almost cat whatever we like atany place of the world. For example people

28、 in Britain can cat bananas from Africa and rice fromIndia. Food is becoming a very big business now根據(jù)短文內(nèi)容選擇最佳答案( )41.Peopleat the beginning ofhuman historyA.could only eat food they eatB. started to farm the landC. developed farming skills( ) 42. People living in Central Europe dont eat s0 much fis

29、h becauseA.they are away from the seaB. they like eating noodlesC. they are near the sea( )43.The underlined（下劃線(xiàn)的）word“conveyin the passage meansin ChineseA.捐贈(zèng)B.傳導(dǎo)C.運(yùn)輸( ) 44. Which ofthe following is TRUE according to the passage?A. People in the south of China eat bananas as their main foodB.People

30、 in India and the Middle East alwaypick up food with their own fingersPeople in Britain can only eat rice from Africa( )45.Whatsthe best title（標(biāo)題）forthepassage？A. Peoples Table Manners(禮儀）B. Peoples Eating ToolsC. People and Food(D) Love is not a single feeling. Although we love our family and frien

31、ds, sometimes we justdont know how to show our love to them.In fact people give love in diferent ways. Each waycan be called a “l(fā)ove language.”46_ First ,offering praise. 47_Praise mcans attention and care.“Youve done a goodjob. cThese shoes look nice on you”.Such praise will make others pleased. 48

32、. _A gift means “I care about you.”The gift does not have to be expensivePerhaps a piece of chocolate is OK Third. spending time together Have a relaxing time and do things we all enjoy. Dont be busyall the time. Have a picnic with the family. 49._ Fourth, being a good learner. 50. _When someone is

33、down， what he wants is tounderstanding Dont talk about ourselves too much.These love languages help us to express love. They also make us understand love form others根據(jù)短文內(nèi)容，將下面方框內(nèi)的句子還原到文中空白處，使短文內(nèi)容完整、通順。（每個(gè)選項(xiàng)只能用一次）A.This kind oflanguage uses words to shoe love.B.Or visit grandparents to talk to them.C

34、.Second, giving gifts. D.Be ready to listen and try to understand.E. Here are some love languages.第卷四、交際應(yīng)用（本題共10分，每空1分）A）從A-G選項(xiàng)中選出能填入空白處的最佳選項(xiàng)補(bǔ)全對(duì)話(huà)。（選項(xiàng)中有兩項(xiàng)是多余的）A:Hi.Jeff_51_B:Im fine, thanks.A：_52_B: Nothing much.A: Would you like to see a movie with me？B:Sure.There are three movie theaters near here.

35、 _53_A:Sun Cinema. Its the closest to us.B: Yes. but what about the long waiting time to get movie tickets？A:_54_We can buy tickets online.B: What do you think of the other cinemas？A: They are not as good as Sun Cinema. It has the biggest screens and the most comfortable seatsB:_55_.A:Well lets go.A

36、.Sounds great.B.You are welcome.C.What are you going to do today？D. How old are you？E.Dont worry.F. How are you?G.Which one shall we go to？51._ 52. _ 53. _ 54. _ 55. _（B）填入一個(gè)適當(dāng)?shù)脑~補(bǔ)全對(duì)話(huà)，每空一詞。A: Hi Mary. Were going to have our graduation (畢 Mk） party._56you decided what to doYet？B: No but we need to rec

37、ord the happiest timeA:lagree.Ill bring my camera hereB:Do you think writing some words to each other isa wonderful idea？A:Yes,I think_57_B:Why _58_ invite our teachers to the party？A:Goodidea.Icant wait.B:Lets get ready for it togetherA:When and_59_shall we meet?B:Lets meet in our classroom at 9:00

38、 a.m. tomorrow.A:All_ 60_. See you!56._ 57. _ 58. _ 59. _ 60. _五、任務(wù)性閱讀（本題共20分）先閱讀（A）（B）（C）三篇短文，然后根據(jù)題目要求及所給語(yǔ)境完成下列五項(xiàng)任務(wù)。(A)achieve, I, climb,much,think about,height,sad,natural It was nearly dark. The sun was going down. A little boy Mike， came back home _61from the mountain “Whats the matter. Mike?”hi

39、s mother asked. “The mountain is so _62_and full ofbig or small stones on the way.I was very tired.Ihadto return Mike cried.” “ It doesnt matter .”his mother said. “ But standing at the top ofthe mountain by_63 is a dream from childhood （童年）！” Mike said His father came up. “What did you notice when

40、_64_ up the mountain？ “ There were a lot of beautiful flowers by the sides ofthe road.” Mike replied. “ Did you feel the beauty of _65 _？” his father asked. Mike _66_the question for a while. “Yes the blue sky the white clouds and the green trees.” Mike answered. “Thats enough!” his father smiled an

41、d said. “Please remember .Son The beautiful scenery（風(fēng)景）is on the way. You have _67_a lot although you didnt reach the top of the mountain. Itis one ofthe _68_ valuable lessons in your life”（B） Afamous writer was born in asmall towAIhOLwas very poor，his parents managed to send him to school. He worke

42、d hard until he left college with good grades He then put his heart into writing. But he made litle money. He couldnt afford his mealssometimes. Publishing （出版） his works was hard for him. An old woman heard of his experiencesShe offered his money. Then he could live on and went on writing. Finally.

43、 his books came outThey sold well. The success of his books brought him great wealh So he made up his mind to help otheryoung writers in the same way. He built up a fund (基金會(huì)）Many young writers received hishelp. Kindness is passed on which makes the world a warm place(C） Every year some birds fly so

44、uth when days turn cold and leaves from trees start to fall. Theytravel a very long way to find a warmer winter This travel is called migration （遷徙） Birds do that because in winter most of the plants die and some insects (昆蟲(chóng)）hide. They flyaway to find enough food. The next year when there is plenty

45、of food for them to eat they willcome backBirds fly in some ways For example, they fly in groups like the letter V or in a row. The tripis often hard and it may be dangerous. But they never get lost because they look at the sun. themoon and stars.The migration of_76_When they fly south Days turn col

46、d and _77_ from trees start to fallWhat the purpose is They fly away in _78_ to find enough food._79_ the trip isIt is often hard and dagerous._80_ they never get lostBecause they look at the sun, the moon and stars.任務(wù)1：閱讀短文（A），用方框中所給詞或短語(yǔ)的正確形式填空，使文章通順、連貫、合理。（每空只能填一個(gè)單詞或一個(gè)短語(yǔ)，每個(gè)單詞或短語(yǔ)限用一次）61._62. _63. _

47、64. _65. _66. _67. _68. _任務(wù)2：閱讀短文（B），根據(jù)英文釋義及首字母提示拼寫(xiě)單詞。69.s_ to make somebody go or be taken to a place70.g _ a mark given in an exam任務(wù)3：閱讀短文（B），進(jìn)行同義句轉(zhuǎn)換，每空一詞。He couldnt afford his meals sometimesHe couldnt afford his meals71. _time 72. _ time 任務(wù)4：根據(jù)短文（B）內(nèi)容回答問(wèn)題。73.Where was the famous writer born？_.74

48、. What did the old woman offer the famous writer?_.75. Did many young writers receive the famous writers help？_.任務(wù)5：根據(jù)短文（C）內(nèi)容完成表格，每空一詞。76._ 77. _ 78. _ 79. _ 80._六、書(shū)面表達(dá)(本題共20分) 假如你是李平，你的英國(guó)筆友Peter因?yàn)閷W(xué)校和家庭中有太多的規(guī)則需要遵守而苦惱。 請(qǐng)你根據(jù)以下信息，給他寫(xiě)一封回信，談?wù)勀愕目捶ǎ⒏嬖V他如何做一名遵守規(guī)則的中學(xué)生。 寫(xiě)作要點(diǎn)： 1 .因他的信任而高興。 2 .你的看法： (1)遵守規(guī)則是重要的

49、： (2)遵守規(guī)則使人受歡迎。 3 .告訴他如何做一名遵守規(guī)則(obey the rules)的中學(xué)生。 寫(xiě)作要求： 1 .不得使用其實(shí)的姓名和學(xué)校名。 2 .可適當(dāng)加入細(xì)節(jié)，使內(nèi)容充實(shí)，行文連貫。 3 .字跡工整、語(yǔ)言精練、表達(dá)準(zhǔn)確、條理清晰。 4 .至少80詞。 Dear Peter, Hows it going?- Best wishes! Yours, Li Ping第 頁(yè)贈(zèng)送:初中數(shù)學(xué)必考定理公式匯編一、數(shù)與代數(shù)數(shù)與式實(shí)數(shù)實(shí)數(shù)的性質(zhì)：實(shí)數(shù)a的相反數(shù)是a，實(shí)數(shù)a的倒數(shù)是（a0）；實(shí)數(shù)a的絕對(duì)值：正數(shù)大于0，負(fù)數(shù)小于0，兩個(gè)負(fù)實(shí)數(shù)，絕對(duì)值大的反而小。二次根式：積與商的方根的運(yùn)算性質(zhì)：（a

50、0，b0）；（a0，b0）；二次根式的性質(zhì)：（2）整式與分式同底數(shù)冪的乘法法則：同底數(shù)冪相乘，底數(shù)不變，指數(shù)相加，即（m、n為正整數(shù)）；同底數(shù)冪的除法法則：同底數(shù)冪相除，底數(shù)不變，指數(shù)相減，即（a0，m、n為正整數(shù)，mn）；冪的乘方法則：冪的乘方，底數(shù)不變，指數(shù)相乘，即（n為正整數(shù)）；零指數(shù)：（a0）；負(fù)整數(shù)指數(shù)： HYPERLINK / （a0，n為正整數(shù)）；平方差公式：兩個(gè)數(shù)的和與這兩個(gè)數(shù)的差的積等于這兩個(gè)數(shù)的平方，即；完全平方公式：兩數(shù)和（或差）的平方，等于它們的平方和，加上（或減去）它們的積的2倍，即；分式分式的基本性質(zhì)：分式的分子和分母都乘以（或除以）同一個(gè)不等于零的整式，分式的值不

51、變，即；，其中m是不等于零的代數(shù)式；分式的乘法法則：；分式的除法法則：；分式的乘方法則：（n為正整數(shù)）；同分母分式加減法則：；異分母分式加減法則：；方程與不等式一元二次方程(a0）的求根公式：一元二次方程根的判別式：叫做一元二次方程（a0）的根的判別式：方程有兩個(gè)不相等的實(shí)數(shù)根；方程有兩個(gè)相等的實(shí)數(shù)根；方程沒(méi)有實(shí)數(shù)根；一元二次方程根與系數(shù)的關(guān)系：設(shè)、是方程 （a0）的兩個(gè)根，那么+=，=；不等式的基本性質(zhì)：不等式兩邊都加上（或減去）同一個(gè)數(shù)或同一個(gè)整式，不等號(hào)的方向不變；不等式兩邊都乘以（或除以）同一個(gè)正數(shù)，不等號(hào)的方向不變；不等式兩邊都乘以（或除以）同一個(gè)負(fù)數(shù)，不等號(hào)的方向改變；函數(shù)一次函數(shù)

52、的圖象：函數(shù)y=kx+b(k、b是常數(shù)，k0)的圖象是過(guò)點(diǎn)（0，b）且與直線(xiàn)y=kx平行的一條直線(xiàn)；一次函數(shù)的性質(zhì)：設(shè)y=kx+b（k0），則當(dāng)k0時(shí)，y隨x的增大而增大；當(dāng)k0時(shí)，y隨x的增大而增大；當(dāng)k0，則當(dāng)x0時(shí)或x0時(shí)，y分別隨x的增大而減??；如果k0時(shí)或x0時(shí)，拋物線(xiàn)開(kāi)口向上，當(dāng)a0時(shí)，如果，則y隨x的增大而減小，如果，則y隨x的增大而增大；當(dāng)a0時(shí)，如果，則y隨x的增大而增大，如果，則y隨x的增大而減??；二、空間與圖形圖形的認(rèn)識(shí)(1)角角平分線(xiàn)的性質(zhì)：角平分線(xiàn)上的點(diǎn)到角的兩邊距離相等，角的內(nèi)部到兩邊距離相等的點(diǎn)在角平分線(xiàn)上。(2)相交線(xiàn)與平行線(xiàn)同角或等角的補(bǔ)角相等，同角或等角的余

53、角相等；對(duì)頂角的性質(zhì)：對(duì)頂角相等垂線(xiàn)的性質(zhì)：過(guò)一點(diǎn)有且只有一條直線(xiàn)與已知直線(xiàn)垂直；直線(xiàn)外一點(diǎn)有與直線(xiàn)上各點(diǎn)連結(jié)的所有線(xiàn)段中，垂線(xiàn)段最短；線(xiàn)段垂直平分線(xiàn)定義：過(guò)線(xiàn)段的中點(diǎn)并且垂直于線(xiàn)段的直線(xiàn)叫做線(xiàn)段的垂直平分線(xiàn)；線(xiàn)段垂直平分線(xiàn)的性質(zhì)：線(xiàn)段垂直平分線(xiàn)上的點(diǎn)到線(xiàn)段兩端點(diǎn)的距離相等，到線(xiàn)段兩端點(diǎn)的距離相等的點(diǎn)在線(xiàn)段的垂直平分線(xiàn)；平行線(xiàn)的定義：在同一平面內(nèi)不相交的兩條直線(xiàn)叫做平行線(xiàn)；平行線(xiàn)的判定：同位角相等，兩直線(xiàn)平行；內(nèi)錯(cuò)角相等，兩直線(xiàn)平行；同旁?xún)?nèi)角互補(bǔ)，兩直線(xiàn)平行；平行線(xiàn)的特征：兩直線(xiàn)平行，同位角相等；兩直線(xiàn)平行，內(nèi)錯(cuò)角相等；兩直線(xiàn)平行，同旁?xún)?nèi)角互補(bǔ)；平行公理：經(jīng)過(guò)直線(xiàn)外一點(diǎn)有且只有一條直線(xiàn)平行于已

54、知直線(xiàn)。(3)三角形三角形的三邊關(guān)系定理及推論：三角形的兩邊之和大于第三邊，兩邊之差小于第三邊；三角形的內(nèi)角和定理：三角形的三個(gè)內(nèi)角的和等于；三角形的外角和定理：三角形的一個(gè)外角等于和它不相鄰的兩個(gè)的和；三角形的外角和定理推理：三角形的一個(gè)外角大于任何一個(gè)和它不相鄰的內(nèi)角；三角形的三條角平分線(xiàn)交于一點(diǎn)（內(nèi)心）；三角形的三邊的垂直平分線(xiàn)交于一點(diǎn)（外心）；三角形中位線(xiàn)定理：三角形兩邊中點(diǎn)的連線(xiàn)平行于第三邊，并且等于第三邊的一半；全等三角形的判定：邊角邊公理（SAS）角邊角公理（ASA）角角邊定理（AAS）邊邊邊公理（SSS）斜邊、直角邊公理（HL）等腰三角形的性質(zhì)：等腰三角形的兩個(gè)底角相等；等腰三

55、角形的頂角平分線(xiàn)、底邊上的中線(xiàn)、底邊上的高互相重合（三線(xiàn)合一）等腰三角形的判定：有兩個(gè)角相等的三角形是等腰三角形；直角三角形的性質(zhì)：直角三角形的兩個(gè)銳角互為余角；直角三角形斜邊上的中線(xiàn)等于斜邊的一半；直角三角形的兩直角邊的平方和等于斜邊的平方（勾股定理）；直角三角形中角所對(duì)的直角邊等于斜邊的一半；直角三角形的判定：有兩個(gè)角互余的三角形是直角三角形；如果三角形的三邊長(zhǎng)a、b 、c有下面關(guān)系，那么這個(gè)三角形是直角三角形（勾股定理的逆定理）。(4)四邊形多邊形的內(nèi)角和定理：n邊形的內(nèi)角和等于（n3，n是正整數(shù)）；平行四邊形的性質(zhì)：平行四邊形的對(duì)邊相等；平行四邊形的對(duì)角相等；平行四邊形的對(duì)角線(xiàn)互相平分

56、；平行四邊形的判定：兩組對(duì)角分別相等的四邊形是平行四邊形；兩組對(duì)邊分別相等的四邊形是平行四邊形；對(duì)角線(xiàn)互相平分的四邊形是平行四邊形；一組對(duì)邊平行且相等的四邊形是平行四邊形。矩形的性質(zhì)：（除具有平行四邊形所有性質(zhì)外）矩形的四個(gè)角都是直角；矩形的對(duì)角線(xiàn)相等；矩形的判定：有三個(gè)角是直角的四邊形是矩形；對(duì)角線(xiàn)相等的平行四邊形是矩形；菱形的特征：（除具有平行四邊形所有性質(zhì)外菱形的四邊相等；菱形的對(duì)角線(xiàn)互相垂直平分，并且每一條對(duì)角線(xiàn)平分一組對(duì)角；菱形的判定：四邊相等的四邊形是菱形；正方形的特征：正方形的四邊相等；正方形的四個(gè)角都是直角；正方形的兩條對(duì)角線(xiàn)相等，且互相垂直平分，每一條對(duì)角線(xiàn)平分一組對(duì)角；正方

57、形的判定：有一個(gè)角是直角的菱形是正方形；有一組鄰邊相等的矩形是正方形。等腰梯形的特征:等腰梯形同一底邊上的兩個(gè)內(nèi)角相等等腰梯形的兩條對(duì)角線(xiàn)相等。等腰梯形的判定：同一底邊上的兩個(gè)內(nèi)角相等的梯形是等腰梯形；兩條對(duì)角線(xiàn)相等的梯形是等腰梯形。平面圖形的鑲嵌：任意一個(gè)三角形、四邊形或正六邊形可以鑲嵌平面；(5)圓點(diǎn)與圓的位置關(guān)系（設(shè)圓的半徑為r，點(diǎn)P到圓心O的距離為d）：點(diǎn)P在圓上，則d=r，反之也成立；點(diǎn)P在圓內(nèi)，則dr，反之也成立；圓心角、弦和弧三者之間的關(guān)系：在同圓或等圓中，圓心角、弦和弧三者之間只要有一組相等，可以得到另外兩組也相等；圓的確定：不在一直線(xiàn)上的三個(gè)點(diǎn)確定一個(gè)圓；垂徑定理（及垂徑定理

58、的推論）：垂直于弦的直徑平分弦，并且平分弦所對(duì)的兩條弧；平行弦?jiàn)A等?。簣A的兩條平行弦所夾的弧相等；圓心角定理：圓心角的度數(shù)等于它所對(duì)弧的度數(shù)；圓心角、弧、弦、弦心距之間的關(guān)系定理及推論：在同圓或等圓中，相等的圓心角所對(duì)的弧相等，所對(duì)的弦的弦心距相等；推論：在同圓或等圓中，如果兩個(gè)圓心角、兩條弧、兩條弦或兩條弦心距中有一組量相等，那么它們所對(duì)應(yīng)的其余各組量分別相等；圓周角定理：圓周角的度數(shù)等于它所對(duì)的弧的度數(shù)的一半；圓周角定理的推論：直徑所對(duì)的圓周角是直角，反過(guò)來(lái)，的圓周角所對(duì)的弦是直徑；切線(xiàn)的判定定理：經(jīng)過(guò)半徑的外端并且垂直于這條半徑的直線(xiàn)是圓的切線(xiàn)；切線(xiàn)的性質(zhì)定理：圓的切線(xiàn)垂直于過(guò)切點(diǎn)的半徑

59、；切線(xiàn)長(zhǎng)定理：從圓外一點(diǎn)引圓的兩條切線(xiàn)，這一點(diǎn)到兩切點(diǎn)的線(xiàn)段相等，它與圓心的連線(xiàn)平分兩切線(xiàn)的夾角；弧長(zhǎng)計(jì)算公式：（R為圓的半徑，n是弧所對(duì)的圓心角的度數(shù)，為弧長(zhǎng)）扇形面積：或（R為半徑，n是扇形所對(duì)的圓心角的度數(shù)，為扇形的弧長(zhǎng)）弓形面積(6)尺規(guī)作圖（基本作圖、利用基本圖形作三角形和圓）作一條線(xiàn)段等于已知線(xiàn)段，作一個(gè)角等于已知角；作已知角的平分線(xiàn)；作線(xiàn)段的垂直平分線(xiàn)；過(guò)一點(diǎn)作已知直線(xiàn)的垂線(xiàn)；(7)視圖與投影畫(huà)基本幾何體（直棱柱、圓柱、圓錐、球）的三視圖（主視圖、左視圖、俯視圖）；基本幾何體的展開(kāi)圖（除球外）、根據(jù)展開(kāi)圖判斷和設(shè)別立體模型；2.圖形與變換圖形的軸對(duì)稱(chēng)軸對(duì)稱(chēng)的基本性質(zhì)：對(duì)應(yīng)點(diǎn)所連的

60、線(xiàn)段被對(duì)稱(chēng)軸平分；等腰三角形、矩形、菱形、等腰梯形、正多邊形、圓是軸對(duì)稱(chēng)圖形；圖形的平移圖形平移的基本性質(zhì)：對(duì)應(yīng)點(diǎn)的連線(xiàn)平行且相等；圖形的旋轉(zhuǎn)圖形旋轉(zhuǎn)的基本性質(zhì)：對(duì)應(yīng)點(diǎn)到旋轉(zhuǎn)中心的距離相等，對(duì)應(yīng)點(diǎn)與旋轉(zhuǎn)中心的距離相等、對(duì)應(yīng)點(diǎn)與旋轉(zhuǎn)中心連線(xiàn)所成的角彼此相等；平行四邊形、矩形、菱形、正多邊形（邊數(shù)是偶數(shù)）、圓是中心對(duì)稱(chēng)圖形；圖形的相似比例的基本性質(zhì)：如果，則，如果，則相似三角形的設(shè)別方法：兩組角對(duì)應(yīng)相等；兩邊對(duì)應(yīng)成比例且?jiàn)A角對(duì)應(yīng)相等；三邊對(duì)應(yīng)成比例相似三角形的性質(zhì)：相似三角形的對(duì)應(yīng)角相等；相似三角形的對(duì)應(yīng)邊成比例；相似三角形的周長(zhǎng)之比等于相似比；相似三角形的面積比等于相似比的平方；相似多邊形的性質(zhì)