(学生版)八下第一章《三角形证明》培优提高(三)

（学生版）八下第一章《三角形证明》培优提高 （三）

八下第一章《三角形证明》培优提高（三）

3、（2012?广州）在 Rt △ AB 中, △ C=90°AC=9, BC=12,则点 C 到 AB 的距离是（ B . 12 25

B . 2 ; 7、（ 2012?贵阳）如图，在RtA AB

C 中，/ ACB=90°,AB 的垂直平分线 DE 交于BC 的延长线于 F,若/ F=30 °, DE=1，则EF 的长是（ ）

一、选择题:

1、已知△ ABC 中，AB = AC, 则^ ABC 的腰和底边长分别为 AB 的垂直平分线交 AC 于D,A ABC 和^ DBC 的周长分别是 60 cm 和38 cm , （ ） A . 24 cm 和 12 cm B . 16 cm 和 22 cm C. 20 cm 和 16 cm D . 22 cm 和 16 cm

2、（2013?郴州）如图，在 Rt△XCB 中，ZACB=90 °, △\=25 °, D 是 AB 上一点.将 使B 点落在AC 边上的B 处，则△XDB 等于（ ）

Rt △KBC 沿CD 折叠, A . 25

C . 35°

D . 40 C. 9

4

4、（2011?恩施州）如图， AD 是△KBC 分别为 50和39,则ZEDF 的面积为（ 的角平分线，DF△XB ，垂足为F ,

）

DE=DG , ZADG 和 △KED 的面积

（2012?广安） 已知等腰^ ABC 中，AD 丄BC 于点D, 且 AD =2BC ， 则^ ABC 底角的度数为（

A . 45

B . 75

C . 45 或 75

D . 60

（2012?毕节地区）如图.在

接CD,若BD=1,则AC 的长是（

RtA ABC 中，/ ）

A=30 °, DE 垂直平分斜边 AC ,交AB 于D , E 是垂足，连 D .

A . 11

B . 第4题 第6题

C . 7

D . 3.

1、如图,△ ABC 中，/ACB= 90° ,CD 丄 AB 于点 D,/ A =

30 ,BD = 1.5cm ,贝U AD=

cm . 二、填空题:

A . 3

B . 2 D. 1

8、（2012?攀枝花）已知实数 X , y 满足|x-4|+ j y 8=0,则以x , y 的值为两边长的等腰三角形的周长是

A . 20 或 16

B . 20 C. 16 D . 以上答案均不对

9、（2012?三明）如图，在平面直角坐标系中，点 A 在第一象限，点 P 在x 轴上，若以P, 0, A 为顶点的

三角形是等腰三角形，则满足条件的点 P 共有（

） A . 2个 B . 3个 C . 4个 D . 5个

10、（ 2012?本溪）如图在直角△ ABC 中，/ BAC=90°, 交边BC 于点E ,连接AE ,则^ ACE 的周长为（ AB=8, ）

AC=6, DE 是AB 边的垂直平分线， 垂足为D , A . 16 B . 15 C . 14 D .

13

（第 10 题） 11、（ 2012?荆门）如图，△ ABC 是等边三角形，P 是/ ABC 的平分线 的垂直平分线交 BC 于点F ,垂足为点Q .若BF=2,贝y PE 的长为（ BD 上一点，PE 丄AB 于点E ,线段BF ）

A . 2

B . 243 C. 43 D. 3 （第 11

匚

4、如图，在△ ABC 中，/ C = 90°,/ B = 15° , AB 的垂直平分线交 BC 于D ,交AB 于E ,若DB = 10cm , 贝U AC = .

5、等腰三角形一腰上的高与另一腰的夹角为 300,腰长为6，则其底边上的高是

6、（2013?泰安）如图，在 RtAXBC 中，△\CB=90 °, AB 的垂直平分线 DE 交AC 于E ,交BC 的延长线于

F ,若 ZF=30 °, DE=1，贝U BE 的长是 ________ .

7、（2005?绵阳）如图，在^ AB （中, BC=5cm, BP CP 分别是△ ABCO △ AC 的角平分线，且 PDAABPE ^ A , 则△PDE 勺周长是 cm .

8、在^ ABC 中, / A=40° , AB=AC , AB 的垂直平分线交 AC 与D,则/ DBC 勺度数为

ABC 中，/ A=30, AB=8,贝U AB 边上的高 CD 的长是

11、（ 2012?常德）如图，在 RgABC 中，/ C=90° AD 是/ BAC 的平分线，DC=2,贝U D 到AB 边的距离 是 .

12、（2012?黔西南州）如图，在^ ABC 中，/ ACB=90°, D 是 BC 的中点，DEX BC, CE// AD,若 AC=2, CE=4, 则四边形ACEB 的周长为 _________________ .

13、（

2012?黑龙江）等腰三角形一腰长为 5, —边上的高为4，则底边长

3 / 8

（填空1） （填空4） （填空6） （填空7）

2、在^ ABC 中，/ A:/B:/ C = 1:2:3 , AB = 6cm ,则

BO cm .

3、等边△ ABC 的周长为12cm ，则它的面积为

cm 2. 9、（2012?襄阳）在等腰△

10、（ 2012?梅州）如图，

/ AOE=/ BOE=15, EF// OB , EC 丄 OB ,若 EC=1,贝U EF=

（填空10（填空11（填空

12

14、（2012?黔东南州）用6根相同长度的木棒在空间中最多可搭成

.

个正三角形15、（2012?佳木斯）等腰三角形一腰长为5, —边上的高为3,则底边长为三、解答题:

1、如图，CEL AB, BF丄AC, CE与BF相交于D,且BD=CD.求证：D在/ BAC的平分线上.

2、如图，ABC中，AB AC, A 50 , DE是腰AB的垂直平分线，求DBC的度数。

3、如下图，CD 丄 AD , CB 丄 AB , AB=AD ，求证：CD=CB .

4、女口图，△

ABC 中,/ B=90° , AB=BC AD 是△ ABC 的角平分线，若 BD=1 求 DC 的长.

C

5、（2012?遵义）如图，△ ABC是边长为6的等边三角形，P是AC边上一动点，由A向C运动（与A、C 不重合），Q是CB延长线上一点，与点P同时以相同的速度由B向CB延长线方向运动（Q不与B重合），

过P作PE丄AB于E,连接PQ交AB于D.

（1）当/ BQD=30时，求AP的长;

（2）当运动过程中线段ED的长是否发生变化？如果不变，求出线段ED的长；如果变化请说明理由

.

6、（2012?珠海）如图，在△ ABC中，AB=AC AD是高，AM是^ ABC外角/ CAE的平分线.

（1）用尺规作图方法，作/ ADC的平分线DN;（保留作图痕迹，不写作法和证明）

（2）设DN与AM交于点F,判断△ ADF的形状.（只写结果）

7、（2012?鄂州）小明是一位善于思考的学生，在一次数学活动课上，他将一副直角三角板如图位置摆放,

A、B、D在同一直线上，EF △KD，△=住DF=90 ° ZC=45 ° 住=60 °量得DE=8，试求BD的长.

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