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八年级下《菱形的性质与判定》练习题及答案

八年级下《菱形的性质与判定》练习题及答案
八年级下《菱形的性质与判定》练习题及答案

2017年八年级数学下册菱形性质与判定练习题

一选择题:

1.下列四边形中不一定为菱形的是()

A.对角线相等的平行四边形

B.每条对角线平分一组对角的四边形

C.对角线互相垂直的平行四边形

D.用两个全等的等边三角形拼成的四边形

2.下列说法中正确的是()

A.四边相等的四边形是菱形

B.一组对边相等,另一组对边平行的四边形是菱形

C.对角线互相垂直的四边形是菱形

D.对角线互相平分的四边形是菱形

3.若顺次连接四边形ABCD各边的中点所得四边形是菱形,则四边形ABCD一定是()

A.菱形

B.对角线互相垂直的四边形

C.矩形

D.对角线相等的四边形

4.菱形的周长为8cm,高为1cm,则菱形两邻角度数比为()

A.4:1 B.5:1 C.6:1 D.7:1

5.四个点A,B,C,D在同一平面内,从①AB∥CD;②AB=CD;③AC⊥BD;④AD=?BC;⑤AD∥BC.这5个条件中任选三个,能使四边形ABCD是菱形的选法有().

A.1种

B.2种

C.3种

D.4种

6.如图,在菱形ABCD中,AB的垂直平分线EF交对角线AC于点F,垂足为点E,连接DF,若∠CDF=24°,则∠

DAB等于()

A.100° B.104° C.105° D.110°

7.如图,在长方形ABCD中,AB=12,AD=14,E为AB的中点,点F,G分别在CD,AD上,若CF=4,且△EFG为等腰直角三角形,则EF的长为()

A.10

B.10

C.12

D.12

8.用一条直线将一个菱形分割成两个多边形,若这两个多边形的内角和分别为M和N,则M+N值不可能是()

A.360°

B.540°

C.630°

D.720°

9.如图,在周长为12的菱形ABCD中,AE=1,AF=2,若P为对角线BD上一动点,则EP+FP的最小值为()

A.1

B.2

C.3

D.4

10.如图,点P是矩形ABCD的边AD上的一动点,矩形的两条边AB、BC的长分别是6和8,则点P

到矩形的两条对角线AC和BD的距离之和是()

A.4.8

B.5

C.6

D.7.2

11.如图,把长方形纸片ABCD折叠,使其对角顶点C与A重合.若长方形的长BC为8,宽AB为4,则折痕EF的长度

为()

A.5

B.3

C.2

D.3

12.如图,四边形ABCD,AD与BC不平行,AB=CD.AC,BD为四边形ABCD的对角线,E,F,G,H分别是BD,BC,AC,AD的中

点.下列结论:①EG⊥FH;②四边形EFGH是矩形;③HF平分∠EHG;

④EG =(BC﹣AD);⑤四边形EFGH是菱形.其中正确的个数是()

A.1个

B.2个

C.3个

D.4个

二填空题:

13.如图,在菱形ABCD中,∠BAD=80°,AB的垂直平分线交对角线AC于点F,E为垂足,连接DF,则∠CDF的度数= 度.

14.如图,正△AEF的边长与菱形ABCD的边长相等,点E、F分别在BC、CD上,则∠B的度数是.

15.把一张矩形纸片ABCD按如图方式折叠,使顶点B和顶点D重合,折痕为EF.若BF=4,FC=2,则∠DEF的度数是.

16.如图,在?ABCD中,对角线AC、BD相交于点O.如果AC=8,BD=14,AB=x,那么x取值范围是.

17.在菱形ABCD中,AE为BC边上的高,若AB=5,AE=4,则线段CE的长为.

18.如图,?ABCD中,AB=2,BC=4,∠B=60°,点P是四边形上的一个动点,则当△PBC为直角三角形时,BP的长为.

三解答题:

19.如图,已知△ABC中,D是BC边的中点,AE平分∠BAC,BE⊥AE于E点,若AB=5,AC=7,求ED.

20.如图,在平行四边形ABCD中,用直尺和圆规作∠BAD平分线交BC于点E(尺规作图的痕迹保留在图中了),连EF.(1)求证:四边形ABEF为菱形;(2)AE,BF相交于点O,若BF=6,AB=5,求AE的长.

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He had a very busy schedule(日程)。But he still s ___________(4) some time visiting the Forbidden City(故宫) and the Great Wall. When a leader visits another c_________(5), he or she sometimes goes to the country’s most f _________(6) places. It is to show respect to the local culture. For rhe leaders, it’s also a good time to r_________(7) during a tiring foreign trip. Obama spent 50 minutes in the Forbidden City on Tuesday. He thinks the Forbidden City is a “magnificent(华丽的) p ________ (8) to visit”. He said: “I will come back with my girls and my wife.” On Wednesday afternoon, he t ________(9) a quick tour of the Great Wall at Badaling. There, he enjoyed a moment of peace. “It’s magical(不可思议的). It reminds(使想到) you o________(10) the sweep(进程) of history,” Obama said about the Great Wall. D Christmas is coming. It’s on December 25. It’s an i_________(1) holiday in many countries, including the US and the UK. Families get t _________(2) to enjoy holiday fun. 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Every evening he passed a poor man near a bridge. The man sat at the side of the road and sold matches(火柴), and there was always an old dog near him. There was a piece of wood around the dog’s neck, and the words”I Am Blind”were written on the piece of wood. Mr Black was a k___________man. He always stopped, said a few kind words to the poor man, and gave him a little money, but he did not take a___________ of his matches. Then one day , Mr Black had a lot of work in his office and was very late. He said, “My train always leaves at five minutes past sic, and it is ten minutes to six now. I’m not going to talk to the poor man today, and I am not going to give him anything. I have given him a lot of money, and I’ve never taken any of his matches. “He came to the man and his dog, but he did not s_________, and he said n_____________. He walked q___________towards the railway station. But the poor man stood up quickly, ran after him and said , “ You haven’t given me anything today. 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