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(完整word版)定义与命题练习题1及答案

(完整word版)定义与命题练习题1及答案
(完整word版)定义与命题练习题1及答案

定义与命题

【知识盘点】

1.能清楚地规定某一名称或术语的句子叫做该名称或术语的______.

2.对某一件事情作出_______判断的句子叫做命题.?每个命题都是由______?和______两部分组成的.

3.如果两条直线平行,那么_________角相等.

4.把命题“对顶角相等”改写成“如果______________________,那么_________________”.5.命题“同角的余角相等”的条件是___________________,结论是_______________________.6.?命题“同底等高的两个三角形面积相等”的条件是__________________________________,??结论是_____________________________________.

【基础过关】

7.下列描述不属于定义的是()

A.两组对边分别平行的四边形叫做平行四边形;

B.正三角形是特殊的等腰三角形;

C.在同一平面内三条线段首尾顺次连接得到的图形叫做三角形;

D.含有未知数的等式叫做方程

8.下列语句不是命题的为()

A.同角的余角相等 B.作直线AB的垂线

C.若a-c=b-c,则a=b D.两条直线相交,只有一个交点

9.命题“垂直于同一条直线的两条直线互相平行”的题设是()

A.垂直 B.两条直线

C.同一条直线 D.两条直线垂直于同一条直线

10.下列语句中,属于命题的是()

A.直线AB和CD垂直吗 B.过线段AB的中点C画AB的垂线

C.同旁内角不互补,两直线不平行 D.连结A,B两点

11.已知下列语句:①天是蓝的;②两点之间线段的长度,叫做这两点间的距离;?③是无理数;④对顶角相等,其中是定义的有()

A.1个 B.2个 C.3个 D.4个

12.已知下列语句:①平角都相等.②画两个相等的角.③两直线平行,?同位角相等.④等于同一个角的两个角相等吗?⑤邻补角的平分线互相垂直.?⑥等腰三角形的两个底角相等.其中是命题的有()

A.2个 B.3个 C.4个 D.5个

【应用拓展】

13.把下列命题改写成“如果……那么……”.

(1)两直线平行,同位角相等.

(2)在同一个三角形中,等角对等边.

(3)两边一夹角对应相等的两个三角形全等.14.对于同一平面内的三条直线a,b,c,给出下列5个判断:①a∥b②b∥c;?③a⊥b;④a ∥c;⑤a⊥c.请以其中两个论断为条件,一个论断为结论,?组成一个你认为正确的命题(至少写两个命题).

【综合提高】

15.一个农妇要过河,随身携带一只小白兔、一篮萝卜和一只饥饿又爱追兔子的狗.她发现系在河边的小船一次只能载她本人和兔子、狗、萝卜其中之一过河,她不能让狗和兔子呆在一起(狗会吓坏可怜的小兔),也不能让小兔和萝卜留在一起(兔子会把萝卜全吃掉),怎么办?请你帮农妇想办法:她怎样来回渡河才能把三样东西安全带到对岸?

【知识盘点】

1._________称为真命题;________称为假命题.

2.经过长期实践后公认为正确的命题叫做________,__________________________叫做定理.3.“能被3整除的整数,它的末位数是3”是______命题(?填“真”或“假”).

4.把“同旁内角互补,两直线平行”写成“如果________,那么________”.

5.“两点之间线段最短”是_________(填“定义”或“公理”或“定理”).

6.“一次函数y=kx-2,当k>0时,y随x的增大而增大”是一个_______命题(填“真”或“假”).【基础过关】

7.下列命题中的真命题是()

A.锐角大于它的余角 B.锐角大于它的补角

C.钝角大于它的补角 D.锐角与钝角之和等于平角

8.下列命题中,属于假命题的是()

A.若a⊥b,b⊥c,则a⊥c B.若a∥b,b∥c,则a∥c

C.若a⊥c,b⊥c,则a∥b D.若a⊥c,b∥a,则b⊥c

9.有下列四个命题:(1)对顶角相等;(2)内错角相等;(3)有两边和其中一边的对角对应相等的两个三角形全等;(4)如果两条直线都垂直于第三条直线,?那么这两条直线平行.其中真命题有()

A.1个 B.2个 C.3个 D.4个

10.已知等腰三角形的一边等于3,一边等于6,则它的周长等于()

A.12 B.12或15 C.15 D.15或18

11.下列说法正确的是()

A.命题一定是正确的 B.不正确的判断就不是命题

C.真命题都是公理 D.定理都是真命题

12.“a、b是实数,若a>b,则a2>b2”显然是错误的,若结论保持不变,怎样改变条件,才能

使之成立?以下四种改法:(1)若a>b>0,则a2>b2;(2)若a>b且a+b>0,则a2>b2;(3)?若ab2;(4)若ab2;其中正确的改法个数是()

A.1个 B.2个 C.3个 D.4个

【应用拓展】

13.判断下列命题是真命题还是假命题,并说明理由.

(1)如果ab>0,那么a>0,b>0.(2)内错角相等.

14.A,B,C,D,E五名学生参加某次数学单元检测,?在未公布成绩前他们对自己的数学成绩进行了猜测.

A说:“如果我得优,那么B也得优”;

B说:“如果我得优,那么C也得优”;

C说:“如果我得优,那么D也得优”;

D说:“如果我得优,那么E也得优”.

成绩揭晓后,发现他们都没说错,但只有三个人得优.请问:得优的是哪三位同学?

【综合提高】

15.如图所示,已知AB⊥BD于点B,ED⊥BD于点D,且AB=CD,BC=DE,那么AC与CE有什么关系?写出你的猜想,并说明理由.

答案:

1.定义 2.正确,题设,结论 3.内错角 4.两个角是对顶角,这两个角相等

5.两个角是同一个角的余角,这两个角相等

6.?两个三角形有公共边且该边上的高线相等,这两个三角形的面积相等

7.B 8.B 9.D 10.C 11.A 12.C

13.(1)如果两直线平行,那么内位角相等

(2)在同一个三角形中,如果两个角相等,那么这两个角所对的两条边也相等

(3)如果两个三角形有两边和它们的夹角对应相等,那么这两个三角形全等

14.若a∥b,b∥c,则a∥c;若a∥b,a∥c则b∥c;若b∥c,a∥c,?则a∥b;

若a⊥b,a⊥c则b∥c;若a⊥b,b∥c则a⊥c;若b∥c,a⊥c则a⊥b

15.先把兔子带到对岸,放下兔子自己返回;再把萝卜(狗)带到对岸,放下萝卜(狗),再带上兔子返回;放下兔子,再带上狗(萝卜)到对岸,放下狗(萝卜),独自返回;最后再带上兔子到对

答案:

1.正确的命题,不正确的命题 2.公理,用推理的方法判断为正确的命题

3.?假 4.同旁内角互补,两直线平行 5.公理 6.真

7.C 8.A 9.A 10.C 11.D ?12.D

13.(1)假命题,当ab>0时,a<0,b<0也成立(2)假命题,画图说明

14.C、D、?E三人

15.垂直且相等,可通过两个三角形全等证明.

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