题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-16270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-11217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-84075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-65097.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-16270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-48254.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-29530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-90829.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211421-35947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211421-76516.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211421-20178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211421-90722.png)
解析
试题分析:(1)由等边对等角,可得∠B=∠C,∠B=∠DAB,即可求得△ABC∽△DBA;
(2)由相似三角形的对应边成比例,即可求得BC的长;
(3)由三角函数的性质,可求得∠B的值,即可求得∠C的值.
试题解析:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-11217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-84075.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211422-25004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211422-89425.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211422-17622.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-16270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-48254.png)
(2)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-16270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211420-48254.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211423-89248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211423-98679.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211421-20178.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211423-31721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211423-62576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211424-19759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211424-19571.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211419-11217.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211424-69104.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211425-35946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211425-71779.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211425-11982.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211425-46065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211422-89425.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211426-84712.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211426-43594.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211426-43594.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211421-90722.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211414-16814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211404-63026.png)
(1)若BD是AC边上的中线,如图1,求
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211404-37638.png)
(2)若BD是∠ABC的角平分线,如图2,求
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211404-37638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211400-30455.png)
(1)如图1,将三角板的直角顶点P在射线OM上移动,两直角边分别与OA,OB交于点C,D.
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211354-37085.png)
①比较大小:PC______PD. (选择“>”或“<”或“=”填空);
②证明①中的结论.
(2)将三角板的直角顶点P在射线OM上移动,一直角边与边OA交于点C,且OC=1,另一直角边与直线OB,直线OA分别交于点D,E,当以P,C,E为顶点的三角形与△OCD相似时,试求
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211354-39764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211354-39764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211354-72089.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102211348-17659.jpg)
A.1 B.2.5 C.2.25 D.1.5
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