八年级数学最新版教材周周清

八年级数学最新版教材周周清
八年级数学最新版教材周周清

八年级下学期周周清一

一、选择题

1.下列各式中①a ;②1+b ; ③2a ; ④32+a ; ⑤12-x ;

⑥122++x x 一定是二次根式的有……………………………( )个。

A . 1 个 B. 2个 C. 3个 D. 4个

2.下列二次根式中,最简二次根式是( ).

(A)

(B)

(C)

(D) . 3. 如果代数式有意义,那么x 的取值范围是…………………( )

A .x≥0

B .x≠1

C .x >0

D .x≥0且x≠1

4、下列各组数中,能构成直角三角形的是( )

A :4,5,6

B :1,1

:6,8,11 D :5,12,23

5、在Rt △ABC 中,∠C =90°,a =12,b =16,则c 的长为( )

A :26

B :18

C :20

D :21

6、△ABC 中,∠A 、∠B 、∠C 的对边分别是a 、b 、c ,AB =8,BC =15,CA =17,则下列结论不正确的是( )

A :△ABC 是直角三角形,且AC 为斜边

B :△AB

C 是直角三角形,且∠ABC =90°

C :△ABC 的面积是60

D :△ABC 是直角三角形,且∠A =60°

7、等边三角形的边长为2,则该三角形的面积为( )

A

::3

8、在□ABCD 中, ∠A:∠B:∠C:∠D 可以是( )

A 1:2:2:1

B 2:1:1:2

C 2:2:1:1

D 2:1:2:1

9、具有下列条件的四边形中,不一定是平行四边形的是( )

A 两组对边分别平行

B 对角线互相平分

C 一组对边平行且相等

D 一组对边平行,另一组对边相等

10.如图,EF 过平行四边形ABCD 对角线的交点O ,并交AD 于E ,交BC 与F ,若AB=4,BC=5,OE=1.5,那么四边形EFCD 的周长是 ( )

A .16

B .14

C .12

D .10

二、填空题

11

= ,

= 比较大小:

-152 12、已知一个直角三角形的两条直角边分别为6cm 、8cm ,那么这个直角三角形斜边上的高为 ;

13、如图,已知一根长8m 的竹杆在离地3m 处断裂,竹杆顶部抵着地面,此时,

顶部距底部有 m ;

14.在□ABCD 中,∠A +∠C =200o ,则∠A =__________;∠B =__________.

15. □ABCD 的周长为120cm ,对角线AC 和BD 相交于点O ,且△AOB 的周长比△

16cm ,则AB =___________,BC=____________

E C O D B A

16. 如图,□ABCD 中,AB ⊥AC, E 为边AD 上的点,G 为AB 的中点,

GF ∥AC 交BC 于点F .若□ABCD 的面积16cm 2,AB=4cm,则△EBC 的面积为__________,△CFG 的面积为__________,△AGF 的面积为_____________,GF= ______cm .

A

B C E F

三、解答题

17、(1

2)

.22

-

18、在t R △ABC 中,∠C=90°. (1)已知c=25,b=15,求a ; (2)已知a=6,∠A=60°,求b 、c.

19、如图,四边形ABCD 是平行四边形,AB=10,AD=8,AC BC,求AC 、OA 以及平行四边形ABCD 的面积

20、□ABCD 中,E 、F 分别在BA 、DC 的延长线上,且AE =21AB ,CF =2

1CD ,试证明AECF 为平行四边形.

21. 如图,在□ABCD 中,点E 、F 是对角线AC 上两点,且AE =CF

求证:∠

EBF =∠FDE .

四: 附加题:

22. 已知:如图,AC 是平行四边形ABCD 的对角线,M N ∥AC ,分别交DA 、DC 于M 、N ,交AB 、BC 的延长线于点P 、Q .求证:MQ=PN .

A B P Q

23. 如图,已知△ABC 是等边三角形,D 、E 分别在边BC 、AC 上,且CD=CE ,连结DE 并延长至点F ,使EF=AE ,连结AF 、BE 和CF 。

(1)请在图中找出一对全等三角形,用符号“≌”表示,并加以证明

(2)判断四边形ABDF 是怎样的四边形,并说明理由。

(3)若AB=6,BD=2DC ,求四边形ABEF 的面积。

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