八年级几何证明练习题

2024-08-03

八年级几何证明练习题（共9篇）

八年级几何证明练习题篇1

能达培训学校内部资料

能达学校八年级数学讲义

姓名：日期： 2006-1-2

4辅助线的添加技巧

人说几何很困难，难点就在辅助线。辅助线，如何添？把握定理和概念。还要刻苦加钻研，找出规律凭经验。图中有角平分线，可向两边作垂线。也可将图对折看，对称以后关系现。角平分线平行线，等腰三角形来添。角平分线加垂线，三线合一试试看。线段垂直平分线，常向两端把线连。要证线段倍与半，延长缩短可试验。三角形中两中点，连接则成中位线。三角形中有中线，延长中线等中线。平行四边形出现，对称中心等分点。梯形里面作高线，平移一腰试试看。平行移动对角线，补成三角形常见。证相似，比线段，添线平行成习惯。等积式子比例换，寻找线段很关键。直接证明有困难，等量代换少麻烦。斜边上面作高线，比例中项一大片。半径与弦长计算，弦心距来中间站。

一、角平分线专题

1．角分线，分两边，对称全等要记全。（牢记，角平分线就是一个对称轴，所以可以将其中的一个△翻转180度，构造全等。也可以应用角分线定理作垂直）基本图形

图一

圆上若有一切线，切点圆心半径连。切线长度的计算，勾股定理最方便。要想证明是切线，半径垂线仔细辨。是直径，成半圆，想成直角径连弦。弧有中点圆心连，垂径定理要记全。圆周角边两条弦，直径和弦端点连。弦切角边切线弦，同弧对角等找完。要想作个外接圆，各边作出中垂线。还要作个内接圆，内角平分线梦圆如果遇到相交圆，不要忘作公共弦。内外相切的两圆，经过切点公切线。若是添上连心线，切点肯定在上面。要作等角添个圆，证明题目少困难。辅助线，是虚线，画图注意勿改变。假如图形较分散，对称旋转去实验。基本作图很关键，平时掌握要熟练。解题还要多心眼，经常总结方法显。切勿盲目乱添线，方法灵活应多变。分析综合方法选，困难再多也会减。

B图二

B图三

例题：

1．已知，CE、AD是△ABC的角平分线，∠B＝60°。求证：AC＝AE＋CD。

2．已知，AB＝2AC，∠1＝∠2，DA＝DB。求证：DC⊥AC。

图二

图三

3．已知，四边形ABCD中，ABCD，∠1＝∠2，∠3＝∠4。求证：BC＝AB＋CD。

4．已知，在△ABC中，∠CAB=2∠B，AE平分∠CAB交BC于E，AB＝2AC。求证：

（1）∠C＝90°；（2）AE=2CE。

图五

5．已知，在RT△ABC中，∠A＝90°，AB＝AC，BD是∠ABC的平分线。求证：BC＝AB＋AD。

6．已知，△ABC中，∠C＝2∠B，AD平分∠A。求证：AB－AC＝CD。

注意：只要看到平分线上的点，要想到向两边作垂线了（点分线，垂两边）

7．已知，在△ABC中，∠A＝90°，AB＝AC，∠1＝∠2。求证：BC＝AB＋AD。

图八

8．已知，AB＞AD，∠1＝∠2，CD＝BC

9．已知，AB＞AD，∠1＝∠2，CE⊥AB，AE＝

2（AB＋AD）。

图十

求证：∠D＋∠B＝180°。

10．已知：∠1＝∠2，∠3＝∠4，求证：AP平分∠BAC。

图十一

2．角平分线＋垂线，角平分线＋平行线，等腰三角形要呈现，线段和差倍分都实现。

图

1图2-1

图2-2

例题

1．已知，∠1＝∠2，AB

＞AC，CD⊥AD于D，H是BC求证：DH＝12

（AB－AC）。

2．已知，AB＝AC，∠BAC＝90°，∠1＝∠2，CE⊥BE。求证：BD＝2CE。

图2

3．已知，∠1＝∠2，CF⊥AE于E，BE⊥AE于E，G为BC中点，连接GE、GF。求证：GF＝GE。

图3

八年级几何证明练习题篇2

A)根据句意和首字母完成句子

1. It is p——to want in line.

2. I like traveling, so I want to be a tour g——

3. Mr King will get a——when someone disturbs his sleep

4. So much c——makes everyone doesn't like to talk with her'.

5. ——Will you send a card to the teacher for the Teachers' Day?

——No, sending a card is not s——enougb!

6． Do you thmk there will be r——in people's homes in the future?

7. I don't know what to do. Could you please give me some a——?

8. She has been skating s

she was five years old.

八年级数学下册证明检测练习题篇3

一、选择题(每小题4分，共32分)

1.下列关于判断一个数学结论是否正确的叙述正确的是 ( )

A.只需观察得出 B.只需依靠经验获得 C.通过亲自实验得出 D.必须进行有根据地推理

2.通过观察你能肯定的是 ( )

A.图形中线段是否相等 B.图形中线段是否平行 C.图形中线段是否相交 D.图形中线段是否垂直

3.下列问题用到推理的是 ( )

A.根据x=1,y=1 得x=y B.观察得到四边形有四个内角

C.老师告诉了我们关于金字塔的许多奥秘 D.由公理知道过两点有且只有一条直线

4.下列句子中,是命题的是 ( )

A.今天的天气好吗 B.作线段AB∥CD C.连结A、B两点 D.正数大于负数

5.下列命题是真命题的是 ( )

A.如果两个角不相等,那么这两个角不是对顶角 B.两互补的角一定是邻补角

C.如果a2=b2,那么a=b D.如果两角是同位角,那么这两角一定相等

6.判断下列命题：①等腰三角形是轴对称图形;②若a>1且b>1，则a+b>2;③全等三角形对应角的平分线相等;④直角三角形的两锐角互余，其中逆命题正确的有 ( )

A.1个 B.2个 C.3个 D.0个

7.已知下列四个命题：(1)若直角三角形的两边长分别是3与4，则第三边长是5;(2) ;(3)若点P(a,b)在第三象限，则点Q(-a,-b)在第一象限;(4)两边及第三边上的中线对应相等的两个三角形全等，其中正确的选项是 ( )

A.只有(1)错误，其他正确 B.(1)(2)错误，(3)(4)正确

C.(1)(4)错误，(2)(3)正确 D.只有(4)错误，其他正确

8.如图，如果AB∥CD，则角α、β、γ之间的关系式为 ( )

A.α+β+γ=360º

B.α-β+γ=180º

C.α+β+γ=180º

D.α+β-γ=180º

二、填空题(每小题4分，共28分)

9.将命题“内错角相等”写成“如果…，那么…”的形式为，

它的逆命题是__________ ______ __ _.

10. 命题“两条对角线互相平分的四边形是平行四边形”的条件是：___________ _____，

结论是：_____________ ______.

11.已知∠1、∠2、∠3分别是△ABC的3个外角，则∠1+∠2+∠3=_______°.

12. 如图，已知∠BDC=1420，∠B =340，∠C=280，则∠A= .

13.有一正方体，将它各面上分别标出a、b、c、d、e、f。有甲、乙、丙三个同学站在不同角度观察结果如图，问这个正方体各个面上的字母的对面各是什么字母，即a的对面为，b的对面为，

c的对面为 .

14.某参观团依据下列约束条件，从A、B、C、D、E五个地方选定参观地点：

(1)如果去A地，那么也必须去B地; (2)D、E两地至少去一处;

(3)B、C两地只去一处; (4)C、D两地都去或都不去;

(5)如果去E地，那么A、D两地也必须去。

依据上述条件，你认为参观团只能去__________________。

15.如图，已知DB平分∠ADE，DE∥AB，∠CDE=82º，则∠EDB= ，∠A= .

三、解答题(每小题10分，共40分)

16.请把下面证明过程补充完整：

已知：如图，DE∥BC，BE平分∠ABC.求证：∠1=∠3.

证明：因为BE平分∠ABC(已知)，

所以∠1=___ ___( ).

又因为DE∥BC(已知)，

所以∠2=__ ___( ).

所以∠1=∠3( ).

17.如图：∠A=65º，∠ABD=∠DCE=30º，且CE平分∠ACB,求∠BEC.

18. 已知如图，在△ABC中，CH是外角∠ACD的角平分线，BH是∠ABC的平分线, ∠A=58°.求∠H的度数.

几何证明与计算习题精选(二) 篇4

（二）2007、1【目标要求】

掌握等腰三角形（包括等边三角形）的判定，能应用等腰三角形的性质（底角相等，顶角平分线、底边上的中线、底边上的高三线合一）进行有关的计算和证明．

能应用直角三角形的重要性质（两个锐角互余，斜边上的中线等于斜边的一半，30°角所对的直角边斜边的一半及其逆定理），以及勾股定理及其逆定理进行有关的计算和证明．【解题指导】例1如图1，已知在△ABC中，点M是边BC的中点，MD⊥AB于点D，ME⊥AC于点E，且MD=ME．求证：△ABC是等腰三角形．

拓展与引申（1）本题的条件不变，还可证明MD等于AB边的高的一半．（2）如果在△ABC中，AB=AC，点M是BC边的任意一点，MD⊥AB于点D，ME⊥AC于点E，这两个条件不变，可证明MD+ME等于AB边上的高．

（3）如图2，在等边△ABC中，P为三角形中的任意一点，那么P到三边的距离之和为定值，这个定值等于等边△ABC高．

例2 如图3，在△ABC中，AB=AC，D、E是AB及AC延长线上的点，连结DE交BC于F，若F是DE的中点，求证：BD=CE．

拓展与引申当点D为AB的中点时，可证明点F是BC的四等分点．

初二数学第1页

（图1）

（图2）

（图3）

例3如图4，在△ABC中，AF平分∠BAC，BF⊥AF于F，CE⊥AF于E，点D是BC的中点．求证DE=DF=

（AB-AC）．

2（图4）

例4 如图5，已知△ABC中，AB=AC，点D在BC边上，∠DAC=90°.（1）（2）

当∠B=30°时，求证：BD=当BD=

CD； 2

CD时，∠B是否一定为30°？ 2

如果一定，请给出证明；如果不一定，请说明理由.（图5）

例5 如图6, 等边△ABC的边长为1, 点D、E分别在AB、BC边上，DE将△ABC分成面积相等的两部分，点F、G在AC边上，DF//BC，EG//AB, 设AF=x,CG=y.（1）求y与之间的函数解析式，并写出它的定义域；

（2）试问以AF、FG、GC的长为三边的长能否构成直角三

角形？请说明理由．

（图6）

拓展与引申如图7，在Rt△ABC中，点D、E分别在AB、BC边上，DE将△ABC分成面积相等的两部分，点F、G在AC边上，DF//BC，EG//AB, 试问以AF、FG、GC的长为三边的长能否构成直角三角形？请说明理由．

（图7）

初二数学第2页

【作业】A组

1．填空题（1）等腰三角形的顶角为α度，那么底角等于度．（2）在ΔABC中，AB=AC=5cm，∠B=60°，那么BC=cm．（3）在ΔABC中，AB=AC=13cm，BC=10cm，那么ΔABC的面积等于cm2．（4）直角三角形两个锐角的度数之比是4∶5，那么较大的一个锐角等于度．（5）如图，在Rt△ABC中，∠ACB=90°，CD是中线，CE是角平分线，∠A=25°.那么∠DCE=________°

（6）等边三角形的边长等于a，那么它的高等于． 2．选择题

（1）用以下长度的三条线段不能组成一个直角三角形的是（）．

（A）6cm，8cm，10cm（B）5cm，12cm，13cm（C）7cm，11cm，15cm（D）8cm，15cm，17cm

（2）在Rt△ABC中，∠ACB=90°，CD、CM分别是这个三角形的高和中线，那么下列结论错误的是（）．

（A）∠ACD=∠B（B）∠MCD =∠ACD（C）∠ACD=∠BCM（D）∠ACM=∠BCD（3）如果一个等腰三角形能够分割为两个小的等腰三角形，那么顶角不可能是（）．

（A）36º（B）72º

（C）90º（D）108º

D 3．如图，把矩形纸片ABCD沿对角线BD折叠，点C落在点E处，BE与AD相交于点F．求证：△BDF是等腰三角形．

4．已知，在矩形ABCD中，AB=4cm，BC=8cm，以点A

为圆心，AD的长为半径画弧，交BC于点E．求∠CDE的度数．

第4题5．在△ABC中，AB=AC，∠B和∠C的平分线相交于点D，求证：点D在边BC的垂直平分线上．

第5题 6．求证：如果一个三角形一边上的中线等于这条边的一半，那

么这个三角形是直角三角形．

7．如图，已知Rt△ABC中，AB=AC，CE垂直∠B的平分线BD，垂足为点E．求证：BD=2CE． B C

（第7题）

初二数学第3页

B组

1．填空题（1）等腰三角形两条边的长度分别为3和6，那么周长等于．

（2）等腰三角形一腰上的高与另一腰所夹的角为45°，那么顶

角为度．

（3）如图，在ΔABC中，BC=5 cm，BP、CP分别是△ABC和△

ACB的平分线，点D、E在BC边上，且PD//AB，PE//AC，那么ΔPDE第1（3）题的周长是_______ cm.．

（4）已知直角三角形的周长为9cm，斜边上的中线长为A 2cm，那么两条直角边长的和为cm．

（5）在Rt△ABC中，斜边AB的垂直平分线MN交边AC于点M，如果∠B=55°，那么∠CBM度．

（6）等腰三角形一腰上的高等于腰长的一半，那么这个B D 等腰三角形的顶角等于_____度．

2．如图，在四边形ABCD中，∠BAD=∠BCD=90°，C

∠ADC=50°，点E是对角线BD的中点．求∠CAE的度数．

第2题

3．在直角坐标平面中，点A的坐标为（-3，0），点B的坐标为（2，5），点C的坐标为（-1，8），试判断△ABC是否为直角三角形，并证明你的结论．

4．如图，已知∠ABD=∠ADB，∠ABC=∠ADC，BE=DC．试比

较∠DCB+2∠ACB与180度的大小． C

5．如图，已知等腰直角三角形ABC中，AB=AC，过点C任意

画一条与斜边相交的直线，分别过点A、B作这条直线的垂线，垂足分别为点D和点E．求证：DE=AD-BE．

C B

第5题

6．已知等腰直角三角形ABC中，∠C=90°，过点C作直线l（直线l不经过点A和点B），过点A作AD⊥l，垂足为点D，过点B作BE⊥l，垂足为点E，试探索DE、AD、BE长度之间的关系．

八年级几何证明练习题篇5

169解：如图所示，先求双曲线斜率为1的弦的中点轨迹，设双曲线斜率为1的弦为AB，且设A（x1,y1）、B(x2,y2)，AB中点M（x,y），则：

x=x1x2yy2,y1且有 222222x1yxy11,221 169169以上两式相减，得

9(x1-x2)(x1+x2)-16(y1-y2)(y1+y2)=0 即9(x1-x2)x-16(y1-y2)y=0 ∵x1-x2=y1-y2

∴9x-16y=0为所求中点所在的直线

x2y21671由16,解得x=± 979x16y0∴轨迹方程为9x-16y=0(x＜－再求a的范围.

上述轨迹与双曲线的交点.

167167或x＞) 77E（1679716797，），F（－，－）7777∵直线ax+y+2=0恒过点D（0，-2）且斜率为-a, 得kDE=927927,kDF= 1616167167或x＞＝的轨迹有公共点，77由图知，已知直线要与方程为9x-16y=0（x＜-则须

kDF＜-a＜99或＜-a＜kDE 1616∴-99279927＜a＜或-＜a＜-1616161699279927,-)∪(-,)

16161616—411— 即a∈(-

新目标八年级（上）期末综合练习篇6

A) 从括号里选出适当的词语，用其恰当的形式填入空白处。(10分)

(instruction, weather, survey, mix, achievement, outstanding, need, lend, autograph, friendly)

1. You may ____ these drinks up.

2. This is headmaster’s ____.

3. I have Yang Ying’s ____.

4. No one came to the sales because the ____ was so bad.

5. China has had a great ____ since 1978.

6. The man in the story is very ____.

7. We did a ____ of our readers.

8. I’m tired. I ____ to have a rest.

9. He likes this book. Please don’t ____ it to others.

10. The boy is ____ in the class.

B) 用所给单词的适当形式填空。(5分)

11. How many ____(tomato) do we buy?

12. The stars in the sky are ____(count).

13. There are some ____(sheep) on that hill.

14. They are American ____(visit).

15. I often go ____(boat) with my classmates.

Ⅱ.单项选择。(15分)

1. The green one is ____ than the yellow one.

A. much expensiveB. much more expensive

C. expensiverD. expensive

2. He speaks English ____ than any other student in his class.

A. wellB. goodC. betterD. best

3. Of all the apples in the basket, this one is ____.

A. redB. redderC. reddestD. the reddest

4. My bike is ____ Lucy’s.

A. as better asB. as good asC. as well asD. as best as

5. The population of Australia is ____ than that of Canada.

A. fewerB. smallerC. largerD. more

6. When the teacher came into the classroom, the students ____ at once. A. stopped to talkB. stopped talking

C. stop to talkD. stop talking

7. It ____ him nearly an hour to get there by bike.

A. spentB. tookC. paidD. used

8. Don’t forget ____ your dictionary next time.

A. to takeB. to bringC. bringD. to get

9. I liked sports ____ I was young.

A. becauseB. whileC. ifD. when

10. If it ____ tomorrow, we’ll go to the Great Wall.

A. isn’t rainB. doesn’t rainC. rainsD. not rains

11. Could you ____ me how to ____ this word in English?

A. tell; speakB. speak; sayC. tell; sayD. say; speak

12. They can’t find the answer ____ this question.

A. forB. withC. toD. of

13. He spends most of his money ____ stamps.

A. onB. forC. inD. by

14. ____ my way home, I bought a shirt ____ my father.

A. By; forB. On; forC. On; toD. Of; to

15. The American people like fried chicken. ____ do we.

A. SoB. SuchC. NeitherD. Either

Ⅲ.情景交际。(10分)

选择适当的答语完成下面的对话。

1. How do you do?

2. Could you come to my party?

3. How long does it take you to make dinner every day?

4. How many bananas do we need?

5. How do you get to school?

6. Where were you born?

7. What’s the time by your watch?

8. What’s the matter with you?

9. Were there any sheep in the field?

10. When did you visit her house?

A. Twenty minutes.

B. I was born in Shanghai.

C. It’s six o’clock.

D. Yes, there were.

E. Three.

F. Yes. I’d love to.

G. Last weekends.

H. I have a toothache.

I. How do you do?

J. By bike.

Ⅳ.句型转换。(10分)

1. She is tall and fat. She has long hair. (合并为一句)

She is ____ tall and fat girl ____ long hair.

2. You should eat more fruit. (改为否定句)

You ____ ____ more fruit.

3. Kate is going fishing on May 2nd. (对划线部分提问)

____ ____ Kate ____ fishing?

4. Mr Wang usually goes to work by bus. (改为同义句)

Mr Wang usually ____ a ____ ____ work.

5. It takes me half an hour to get to the shop. (对划线部分提问)

____ ____ ____ it take ____ to get to the shop?

6. His bike is new. My bike is newer. (合并为一句)

My bike is ____ ____ ____.

7. Peel the bananas and apples. (改为否定句)

____ peel the bananas ____ apples.

8. We have a good time every day. (用last Sunday改写句子)

We ____ a good time last Sunday.

9. He went to school when he was 7 years old. (对划线部分提问)

____ did he ____ to school?

10. They are going to have an English party this evening.

(对划线部分提问)

____ are they going to ____ this evening?

Ⅴ.英汉互译。(10分)

1. 多数学生每天晚上在家做作业。

________________________

2. 当你疲劳时，你应该听听音乐。

________________________

3. 盒子里有不同的东西。

________________________

4. 他花了两天的时间看这本书。

________________________

5. 明天我不得不帮母亲打扫房间。

________________________

6. Kate likes to wear the same clothes with me.

________________________

7. How many sandwiches did you eat yesterday?

________________________

8. I went to the Summer Palace the day before yesterday.

________________________

9. She started skating at the age of five.

________________________

10. It’s fine today. How about going fishing?

________________________

Ⅵ.完形填空。(10分)

Who is your idol(偶像)? Why do you like the person? Cool looks? Money? A lot of talent?

Shanghai teenagers say they __1__ more than that. Most of them say their idols are hardworking and brave(勇敢).

This summer, Shanghai’s Xinwen Evening News __2__ around 1,000 middle school students about their idols.

The newspaper __3__ people in six different groups: leaders, young heroes, teenagers, writers, artists and business people. Students were asked to __4__ one from each group.

NBA __5__ Yao Ming was the No. 1 Chinese idol __6__ 48% of all votes (投票).

Popular singer Jay Chou(周杰伦) is the teen’s __7__ star. A teenager said, “Jay is so kind to his mother and grandma. He __8__ good care of them.”

Shanghai students also like U.S. businessman Bill Gates. More than half picked him as their idol. A junior student who likes Gates said, “Bill was not __9__ rich. He worked hard. And he doesn’t like to tell everyone how rich he is. He also has courage(勇气). He __10__ school to start his own business!”

1. A. look upB. look afterC. look atD. look for

2. A. askedB. talkedC. spokeD. told

3. A. getB. keepC. putD. play

4. A. pickB. pick upC. hopeD. give

5. A. writerB. starC. businessmanD. leader

6. A. inB. withC. byD. for

7. A. bestB. funnyC. favoriteD. pleasant

8. A. looksB. paysC. drawsD. takes

9. A. keptB. hopedC. bornD. wanted

10. A. leftB. returnedC. went toD. went out

Ⅶ.阅读理解。(20分)

(A)

Two tramps(流浪汉) were sleeping under a tree by a busy main road when a large expensive car drove up and a man stepped out, walking up to the two tramps and waking them up.

“Just look at what you are doing there! ”the man began to say. “If you get up and look for a job, then you can live a better life. You might even become rich like me. By the time I was 40, I had become a leader (领导) of the company and now I am 60 and I am rich and can retire (退休).”

One of the tramps looked at him over and answered, “And if we had done all those things, we could also retire and sit under a tree and watch rich men driving by in expensive cars.”

1. The two tramps were waken up by ____.

A. a treeB. a manC. a busy roadD. a car

2. How did the man feel about the tramps? ____.

A. He took pity (可怜；同情) on them

B. He was proud of them

C. He felt happy for them

D. He showed his love to them

3. The man wanted the tramps to ____.

A. make a better lifeB. become a leader

C. have dinner with himD. retire at 60

4. The two tramps ____.

A. liked to go begging(乞讨)B. were very sad for their life

C. enjoyed their lifeD. admired(羡慕) the rich man

5. We can infer(推断) that ____.

A. the two tramps would try their best to find a job and live a better life

B. the man would give the two tramps a lot of money to spend

C. the man would do as the tramps did

D. the two tramps would do as they used to

(B)

Today the children of this country at last returned to work. After a two-month holiday pupils have started a new term. How many adults (成年人) get such a long holiday? Two or four weeks in the summer and public (公共的) holidays—that’s all working men get. For most women, they are not lucky to have a holiday at all.

Children don’t need such a long holiday. In term time they start work later and finish earlier than anyone else. In holidays most of them get bored(厌烦), and some get into trouble. What a waste!If their parents were given more free time instead, everyone would be happier. This is not just a national problem either—it is worldwide. Dates may be different from country to country, but the pattern(模式) is the same. Why should children do half as much work and get twice as much holidays as their parents?

1. Most working men get ____ weeks in the summer and public holidays. A. three and fiveB. two or fourC. four and sixD. two or six

2. From the passage we know that ____.

A. it is not easy for a woman to get a holiday

B. most women have holidays

C. no woman gets holidays

D. most men don’t have holidays

3. The writer thinks children ____.

A. must have such a long holiday

B. should have a long holiday

C. don’t need such a long holiday

D. should get into trouble in holidays

4. How long do children have for their holidays? ____.

A. Two weeks

B. Two days

C. Half of their parents’ holidays

D. Twice of their parents’ holidays

5. Children in ____ have long holidays.

A. few countriesB. many countries

C. just this countriesD. a few of countries

Ⅷ.书面表达。(10分)

根据所给文字提示，写一篇50—80个词的短文：

1. 假设你是李磊，你给你的美国朋友Bill写一封信，介绍你是如何学习

英语的。

2. 要求内容完整，书写规范，表达准确，标点正确，卷面清楚整洁。

3. 至少写五句话以上，多者不限，信的开头已经给出。

4. 关键词：favorite subject, work hard, practise reading, speaking, listening, writing, keep on doing, remember words, listen to…, watch English videos, talk in English (答卷时，不必局限于所给的关键词，可以根据自己的实际情况适当发挥。)

Dear Bill,

How are you? Today I want to tell you about my English study._____

________________________________________________________________

__________________________________________

八年级几何证明练习题篇7

1.(本小题满分20分)

如图:EB,EC是O的两条切线,B,C是切点,A,D是

O上两点,如果E46,DCF32,试求A的度数.第1题图

2、(本小题满分20分)如图,△ABC中,AB=AC,AD是中线,P为AD上一点,CF∥AB，BP延长线

交AC、CF于E、F,求证: PB2=PE•PF．

3.(本小题满分20分)

已知:如右图,在等腰梯形ABCD中,AD∥BC,AB＝DC,过点D作AC的平行线DE,交BA的延长线于点E． E 求证：(1)△ABC≌△DCB

(2)DE·DC＝AE·BD．

C 第2题图

第3题图

4.(本小题满分20分)

如图,⊙O的直径AB的延长线与弦CD的延长线相交于点P,E为⊙O上一

AEAC,DE交AB于点F,且AB2BP4,求PF的长度.点,

E F B 第4题图

5.(本小题满分20分)

如图,A是以BC为直径的O上一点,ADBC于点D,过点B作O的切线,与CA的延长线相交于点E，G是AD的中点,连结CG并延长与BE相交于点F,延长AF与CB的延长线相交于点P.(1)求证:BFEF；

(2)求证:PA是O的切线；

(3)若FGBF,且

O的半径长为求BD和FG的长度.高中数学第十五单元测试题答案

选修4-1 几何证明选讲

1．【解析】连结OB,OC,AC,根据弦切角定理,可得ABACCAD

第5题图

(180E)DCF673299

22、【解析】连结PC,易证PCPB,ABPACP

∵CF//AB ∴FABP,从而FACP 又EPC为CPE与FPC的公共角,CPPE

∴PC2PEPF 

FPPC

又PCPB, ∴PB2PEPF,命题得证.从而CPEFPC,∴

3．【解析】证明：(1)∵四边形ABCD是等腰梯形，∴AC＝DB ∵AB＝DC，BC＝CB，∴△ABC≌△BCD

(2)∵△ABC≌△BCD，∴∠ACB＝∠DBC，∠ABC＝∠DCB ∵AD∥BC，∴∠DAC＝∠ACB，∠EAD＝∠ABC

∵ED∥AC，∴∠EDA＝∠DAC∴∠EDA＝∠DBC，∠EAD＝∠DCB ∴△ADE∽△CBD∴DE:BD＝AE:CD，∴DE·DC＝AE·BD.4【解析】连结OC,OD,OE,由同弧对应的圆周角与圆心角之间的关系

AEAC可得结合题中条件

CDEAOC,又CDEPPFD, AOCPC,从而PFDPCO, PFPD

故PFDPCO,∴, 

PCPO

由割线定理知PCPDPAPB12,故PF

E F B PCPD12

3.PO4

5．【解析】(1)证明：∵BC是O的直径，BE是O的切线，∴EBBC．又∵ADBC，∴易证△BFC∽△DGC，△FECBFCFEFCF

． ∴DGCGAGCGBFEF

． ∴

C DGAG∵G是AD的中点，∴DGAG． ∴BFEF．

(2)证明：连结AO，AB．∵BC是在Rt△BAE中，由（1），知F是斜边BE的中点，∴AFFBEF．∴FBAFAB．又∵OAOB，∴ABOBAO． ∵BE是O的切线，∴EBO90°．

∵EBOFBAABOFABBAOFAO90°，∴PA是O的切线．

(3)解：过点F作FHAD于点H．∵BDAD，FHAD，∴FH∥BC．由(1)，知FBABAF，∴BFAF．

由已知，有BFFG，∴AFFG，即△AFG是等腰三角形．

HG1

． ∵FHAD，∴AHGH．∵DGAG，∴DG2HG，即

DG2

∵FH∥BD，BF∥AD，FBD90°，∴四边形BDHF是矩形，BDFH．

FHFGHG，即∵FH∥BC，易证△HF∽△GD．∴

CDCGDG

BDFG1HG

．

CDCG2DG

∵

O的半径长为

∴

BC∴

解

得

BD

．

BDBD1

． CDBCBD2

FGHG1

．∵，∴BDFH

CGDG2

∴FGCG．∴CF3FG．

222

在Rt△FBC中，∵CF3FG，BFFG，由勾股定理，得CFBFBC．

七年级下-几何说理题专项练习篇8

（1）．如图，∠1=120°，∠BCD=60°，AD与BC为什么是平行的？（填空回答问题）解：∵∠1+∠2=__________，(_________).又∠1=120°（已知），∴∠2=____________.∵∠BCD=60°(_________).∴∠BCD=∠ __________.∴ AD∥BC(___________________________)（2）、如图，已知AD∥BE，AE 因为AD∥BE（）

所以A_______180（）因为AE（已知）

所以______________180（）所以DE∥AC（）所以1_______（）

（3）．如图，AD⊥BC于D，EG⊥BC于G，∠E=∠3，试说明：AD平分∠BAC。解：因为AD⊥BC，EG⊥BC(_________).所以∠EGD＝90°，∠ADC＝90°（）所以∠EGD＝∠ADC（）

所以∥（）所以∠1=∠E（）

∠2=∠3（）又因为∠3=∠E

所以∠1=∠2（————————）

所以AD平分∠BAC（）

（4）.如图已知BE平分∠ABC，E点在线段AD上,∠ABE=∠AEB AD与BC平行吗?为什么?

解：因为BE平分∠ABC（）所以∠ABE=∠EBC（）因为∠ABE=∠AEB（）所以∠AEB=∠EBC()所以AD∥BC（）（5）．如图，已知AB∥CD，∠E=90°，那么∠B＋∠D是多少度？为什

么？

解：过点E作EF∥AB，得∠B＋∠BEF=180°（），因为AB∥CD（），EF∥AB（所作），2D

ABE 3 B

A1 G D

第24题图

所以EF∥CD（）．得（两直线平行，同旁内角互补），所以∠B＋∠BEF＋∠DEF＋∠D=°（等式性质）．即 ∠B＋∠BED＋∠D=°．因为∠BED=90°（已知），所以∠B＋∠D=°（等式性质）．（6）．如图：已知EFAB,CDAB,1=3,那么DG//BC吗？为什么？解：因为EFAB,CDAB（已知）

所以EF//CD(___________________________)

所以_______________(____________________________)

E因为1=3（已知）

所以_____________(____________________________)B

所以DG//BC(________________________________)（7）．如图：已知DAB=DCB,AE,CF分别平分DAB，DCB，且AE//CF,问：DC//AB吗？ E

解：因为AE,CF分别平分DAB，DCB（已知）C

所以1=

12DAB, 2=

1DCB A

(_____________________)

因为DAB=DCB（已知）

所以____________(______________________)又因为AE//CF（已知）

得______________________(____________________________)所以______________________(____________________________)所以DC//AB(_________________________________)

（8）.已知，如图，BE平分∠ABC,DE∥BC，∠3=35°，求∠1的度数解：因为BE平分∠ABC(已知)

所以（角平分线意义）因为DE∥BC（已知）

所以（）

所以

（）

因为∠3=35°（已知）所以∠1=°

（9）.如图，∠A=∠D,∠C=∠F试说明：BF∥CE 解：因为∠A=∠D（）所以DF∥AC（）

所以(_________).又因为∠C=∠F（已知）

所以（等量代换）A

所以(_________).（10）、如图EF∥AD，∠1=∠2，∠BAC=70 o，求∠AGD。解：∵EF∥AD，∴∠2=（）又∵∠1=∠2，∴∠1=∠3，∴AB∥（）∴∠BAC+=180 o（）∵∠BAC=70 o，∴∠AGD=。（）（11）如图，已知∠BED=∠B+∠D，试说明AB与CD的关系。解：AB∥CD，理由如下：

过点E作∠BEF=∠B ∴AB∥EF（）∵∠BED=∠B+∠D ∴∠FED=∠D ∴CD∥EF（）∴AB∥CD（）（12）．如图，∠G＝28°，∠AEF＝58°，∠FDG＝30°，说明AB//CD的理由。解：∵∠G＝________°，∠FDG＝_________°（已知）

∴∠CFG＝________°＋________° AEB＝________°（___________________________）

又∵∠AEF＝58°（已知）

F∴∠_______＝∠________

∴_________//_________（__________________________）G（13）、如图，已知OP平分AOB，MN∥OB，AOB620，求3的度数．解：因为OP平分AOB（），又因为AOB620

（），所以（）．

因为MN∥OB（），所以（）．所以30（）．

（14）．如图，已知AB∥DE，∠1=∠2，那么AE与DC平行吗？为什么？

21E

（15）、如图，EB∥DC，∠C=∠E，请你说出∠A=∠ADE的理由。

16）、如图，已知BAPAPD1800，12，问EF吗？请说明理由．

（18）.已知：∠AED=∠C，∠DEF=∠B，请你说明∠1与∠2互补.A

D E

B C

（19）、如图，AD是∠EAC的平分线，AD∥BC，∠B=30 o，求∠EAD、∠DAC、∠C的度数。

（20）．如图，已知 AB // CD，1(4x25)，2(85x)，求∠1的度数．E

A B

（21）.如图,直线AB与CD相交于一点O,OE平分∠BOD，OF⊥F

于点O,若∠AOC=60°，（求∠COF的度数.（22）.如图，已知直线a∥b，1(4x60),2(6x30),F

第23题

求∠

1、∠2的度数.a

2第24题

（23）.如图，已知AB∥EF，∠1=∠2，那么AB与CD平行吗？为什么？请说明理由.E

第26题

2（24）．如图：已知AB//CD,AB//EF

（1）CD//EF吗？为什么？

（2）若A=110,ACE=50,求E的度数

八年级几何证明练习题篇9

1. Last week we ____ a survey of our listeners on the programs.

A. didB. doC. areD. were

2. This theatre has the biggest screens and ____ seats.

A. comfortableB. comfortablest

C. most comfortableD. the most comfortable

3. I like Easy Listening 97.3 FM because it ____ the most interesting music.

A. haveB. playsC. playD. is

4. I’m really hungry. Where should we go ____ lunch?

A. atB. withC. forD. to

5. Then you can decide ____ the best place to visit.

A. onB. atC. aboutD. in

6. His sister Elizabeth is ____ person I know. Do you agree?

A. a funnyB. the funnyC. a funnierD. the funniest

7. Do you know who won the prize ____ the best actor?

A. withB. forC. atD. in

8. Sometimes my daughter even dances ____ music. It’s really cute.

A. andB. not haveC. withoutD. with any of the

9. Look!The little girl is dancing ____ the music we are listening to.

A. atB. toC. forD. in

10. It’s cold there. We ____ some warm clothes.

A. should to takeB. need take

C. need to takeD. should taking

11. Easy Listening ____ a program that I could enjoy.

A. listens likeB. hears likeC. sounds likeD. listens to as

12. Next year we ____ a nice teacher called Miss Yang.

A. haveB. had

C. are going to haveD. should have

13. Your hair looks ____ than Li Mei’s. Do you believe it?

A. shortB. a little short

C. a little shorterD. a little more shorter

14. I think you ____ warm clothes because it’s cold outside.

A. need wearB. need to wear

C. need wearingD. should wearing

15. On weekends she usually invites some friends to her house ____

games.

A. playedB. playingC. and playsD. to play

16. Charlotte, I really have ____ to tell you. Listen carefully.

A. something importantB. important something

C. nothing importantD. important anything

17. He is very glad because he won the prize ____ the best singer.

A. atB. inC. withD. for

18. Everyone knows we can’t live ____ air or water.

A. withoutB. having notC. no havingD. not with

19. I really like this department store because it has ____ service.

A. the friendlierB. the friendliest

C. the more friendlierD. a most friendly

20. Do you do any chores at home? I hate ____ the chores.

A. to doB. aboutC. I doD. if I should do

21. Emilia, don’t forget ____ your father to pick you up tonight.

A. tellingB. and tellC. aboutD. to tell

22. I have a favor to ask you. Could you ____ my dog ____ this

evening?

A. take, for a walk B. have, for a walk

C. bring, for walksD. give, some walks

23. Please ____ yourself when I am away these days.

A. take care ofB. care on

C. have care aboutD. give cares for

24. I think fifty yuan ____ enough for Cindy to buy a doll.

A. isB. areC. beD. to be

25. I write ____ you that I’m going to visit you next month.

A. and tellB. tellingC. to tellD. for telling

Ⅱ.据意填词

1. Shenyang is the capital city of Liaoning ____.

2. It seldom rains ____ snows in Beijing. It’s dry here.

3. I think thirty dollars is ____ for us to buy all the books we need.

4. Many people like to visit Sanya because it has beautiful ____.

5. This shirt is only twenty yuan. It’s the ____ one I saw today.

6. I don’t like All Talk 970AM. I think it has the ____ music.

7. This bookstore is not near. It’s ____ than that one.

8. It’s cold at night but it becomes hot in the ____.

9. My son loves action movies but I don’t often go to ____ them.

10. Last time Cindy won the first ____ for the best performer.

Ⅲ.补全对话

A: Are you hungry?

B: Ah, yes. But where should we go this time?

A: Fatty’s is the __1__. Let’s go there, OK?

B: Yes, it’s really close to our school. But it’s the __2__ expensive.

A: Yes, it’s a little expensive. But what is the best place __3__ have lunch?

B: I think we __4__ go to the Tommy’s.

A: But how __5__ is it from school, do you know?

B: It’s about ten minutes from here __6__ bus.

A: Is the service good? And is its food good, too?

B: Yes, I think it has the __7__ service and the food is delicious.

A: But __8__ much is a meal? Is it very expensive?

B: Don’t worry about it. I think it is the __9__ one I know and it has friendliest __10__.

A. Oh, really? Let’s go there then.

Ⅳ.完形填空

Man has a big brain. He can think, learn and speak.

Scientists once thought that men are different from animals __1__ they can think and learn. They know now that dogs, monkeys, birds can learn too.

They are beginning to understand that men are different from animals because they can speak. Animals can’t speak. They make noises when they are afraid, or unhappy. Apes(类人猿) can understand some things __2__ than man. One or two of them have learned __3__ words. But they can not join words up to make sentences. They cannot think __4__ us because they have __5__ language. Language is a wonderful thing. Man has __6__ build a modern world because he has language. __7__ child can speak his own language very well when he is four or five, __8__ no animals learn to speak. __9__ do children learn it? Scientists don’t really know. __10__ happens inside our body when we speak? They don’t know. They only know that man can speak because he has brain.

1. A. afterB. ifC. beforeD. because

2. A. quicklyB. much quicklyC. more quicklyD. quicker

3. A. fewB. a fewC. littleD. a little

4. A. asB. aboutC. likeD. over

5. A. notB. anyC. noD. some

6. A. to able toB. be able toC. able toD. been able to

7. A. EachB. EveryC. OneD. All

8. A. orB. soC. andD. but

9. A. HowB. WhatC. WhyD. Which

10. A. WhereB. WhenC. WhatD. How

Ⅴ.阅读理解

(A)

一个小男孩用镜子钓鱼真是天下奇闻，你想不想学习一下他先进的钓鱼技术呢？那么就请阅读下文，让我们一起来欣赏他的绝活吧！

A man saw a boy standing beside a lake with a mirror. “Excuse me”, he said, “but could you tell me what you’re doing?”

“I’m fishing.”

“With a mirror? Could you tell me how it works?” the man asked.

“OK, but I want five dollars.”

The man wanted to know the secret very much, so he handed the boy the money. “Now show me how it works,” he said.“Well,” the boy began, you hold the mirror towards the water, and when a fish goes by the sunlight the mirror gives him a surprise. He stops and doesn’t know what to do and then you catch him at once. The man was surprised, “Can you really catch fish with the mirror? How many did you catch?”

“You’re the fifth today!” replied the boy.

Notes:

1. mirror n. 镜子

2. hold v. 拿

根据短文内容，判断正（T）误（F）

1. The man wanted to look at the boy’s mirror.

2. The man gave the boy five dollars.

3. The boy caught five fish that day.

4. The boy got fifteen dollars that day.

5. When the man heard the boy’s words, he would be very happy.

(B)

事情都要认真对待，下文中的主人公Ben是怎样生病的呢？你从中一定会有深刻体会的。

Soap for Dinner

Ben was home from work and opened his mailbox. There was a yellow bottle of soap—soap for washing dishes. The dish soap was a free sample from a soap company. It was a kind of new soap with a little orange juice in it. The company wanted people to try it.

There was a picture of two oranges on the label. Over the oranges were the words “with Real Orange Juice”. Ben was happy. “I’m going to eat a salad for dinner,” he thought. “I can put some of the orange juice in my salad.” So he put the soap on his salad and ate it.

A bit later he was sick. A lot of people put the soap on fish, on salads, and in their tea. Later, they were sick, too.

What can we learn from Ben’s story? Read labels carefully. And don’t eat soap for dinner.

Notes:

1. soap n. 肥皂

2. label n. 标签

3. mailbox n. 邮箱

4. salad n. 沙拉

5. sample n. 样品

根据短文回答问题：

1. What was in the yellow bottle?

2. What was on the label?

3. What did Ben put into his salad?