八年级上学期月考试卷

一选择题：（共12题，每题3分，共36分）

1.下列哪组数据能构成三角形（）。

A.1cm,2cm,3cm;

B.4cm,4cm,9cm;

C,3cm,4cm,5cm; D.2cm,3cm,5cm.

2. 如图所示，BD,CE是?ABC的高，则下列错误的结论是（）。 A

A. ∠ACE=∠ABD;

B. ∠BFC+∠ACE+∠ABD=180° E F D

C.∠BFC=180-∠A;

D.∠DFC+∠ACE+∠BFE+∠ABD=180°B C

3.小强利用全等形的知识测量池塘两端M，N的距离，如果?PQO≌?NMO,则只需测出其长度的线段是（).

A. PO;

B. PQ;

C. MO;

D. MQ.

4.一个多边形的每个内角都相等，每个内角与相邻的外角

的差为100°，那么这个多边形是（）。

A.七边形；

B.八边形；

C.九边形；

D.十边形。Q

5.下列说法，其中正确的个数是（）。

①等边三角形是等腰三角形；

②一个三角形至少有两个锐角；

③三角形外角和大于这个三角形的内角和；

④四边形的内角最多可以有三个钝角；

⑤多边形的对角线有7条.其中正确的个数是（）。

A. 2;

B. 3;

C. 4;

D. 5.

6.若从一个多边形的一个顶点出发最多可画2015条对角线，则它是（）。

A .2015边形；

B 。2016边形；C.2017边形； D.2018边形.

7.图中的两个三角形全等，则∠α=（）

A .72°；B. 60°；60° a

C.58°；

D.50°。 c a

58°62° c

8.如图，已知：CB=FE，∠CBA=∠FED,下列条件中不能判定?ABC≌?DEF的是（）。

A.AC=DF;

B.∠C=∠F; C F

C.AB=DE;

D.AC∥DF.

A D

B E

9.如图，PD ⊥ AO 于D ，PE ⊥BO 于E ，下列条件 A

①OP 是∠AOB 的平分线；②DO=EO ；③PD=PE ； D ④∠OPD=∠OPE ；选一个能够证明?DOP ≌?EOP P

的条件的有（）。 O

A. 1 个；

B. 2个；

C. 3个；

D. 4 个。 E B

10.点P 在∠AOB 的平分线上，点P 到OA 边的距离等于2，点Q 是OB 边上的任意一点，

下列选项正确的是（ )。 A

A. PQ>2 ；

B. PQ<2；

C. PQ ≥2；

D. PQ ≤2。

11.如图所示,在?ABC 中，AD ⊥BC,

CE ⊥AB 垂足分别为D.E ，AD,CE 交于 E

点H ，已知EH=EB=6，AE=8，则CH

的长是（）。 H

B D C

A. 2 ;

B. 4; C , 6 ; D . 8.

12.如图，在?ABC 中，AD 是∠A 的外角平分线，

P 是AD 上异于A 的任意点，设PB=a,PC=b,AB=m, A

AC=n,则（m+n)于（b+c)的大小关系是（）。

A .m+n>b+c ；B. m+n=b+c ； P

C.m+n< b+c ；

D.无法确定。

B C D

二．填空题：（共8题，每题3分，共24分）

13.铁栅门和多功能挂衣架能够伸缩自如，是利用了四边形的。

14.等腰三角形的两边长分别为3和6，则周长为。

15.直角三角形两锐角平分线相交所成的钝角的度数是。

16.如图钝角三角形ABC 和钝角三角形A ′B ′C ′中，AD,A ′D ′分别是边BC,B ′C ′上

的高，且AC=A ′C ′,AD=A ′D ′，要使 ?ABC ≌△A ′B ′C ′,则应补充条件

.。（填写一个即可）

17.如图所示，BE ⊥AC,垂足为D,且AD=CD,BD=ED,若∠ABC=68°，则∠E= 。

18如图，在?ABC 中，∠C=90°，∠CAB=48°，按一下步骤作图：①以点A 为圆心，小

于AC 的长为半径画弧，分别交AB. AC 于点E. F ；②分别以点E. F 为圆心，大于2

1EF 的长为半径画弧，两弧相交于点G ；③作射线AG 交BC 边于点D 。则∠ADC 的度数为。

E A

A A ′

B D

C B ′

D ′ C ′ C B （第16题图） (第17题图)

19.三角形两边分别为6和8，则第三边上的中线m的取值范围是。

20.如图，在Rt?ABC中，AC=6cm,BC=8cm,∠ACB=90°，点P. Q分别同时从B点沿线段BC和BC的垂线BX上运动，点P的速度为1cm/s,当点Q的速度为时，?ABC和?PQB全等。X

C A Q

F D

A B C B

E P

（第18题图）（第20题图）

三．解答题：

21.一个多边形的内角和比外角和多540°，求这个多边形的边数。（8′）

22.一次数学课王老师在黑板上画出图，并写出了下列四个等式：

(1)AB=DC ；（2）BE=CE； A D

（3）∠B=∠C；（4）∠BAE=∠CDE；

要求同学从四个等式中选出两个作为条件推出 E

AE=DE。（10′）

已知： B C

求证：AE=DE。

证明：

23.如图的三角形纸片中，AB=10cm, BC=8cm，AC=5cm，沿过点B的直线折叠这个三角形，使点C落在AB边上的点E处，折痕为BD，求?AED的周长。（10′）

A E B

24.在四边形ABCD中，AC平分∠BAD，过C作CE⊥AB于E,并且BC=DC,求∠ABC+∠ADC 的度数。（10′）

A E

25.如图，在?ABC中，D是BC的中点，∠BAD=∠CAD，求证：AB=AC.(10′)

B D C

26.如图，在Rt?ABC中，∠BAC=90°，AB=2AC,点D是AB的中点，将一块锐角为45°的直角三角板如图放置，使三角板斜边的两端点分别与A. D重合，连接BE. EC,试猜想线段BE与EC的关系，并证明你的猜想。(12′)

E A

B C

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