题目
题型:期末题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051506-15214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051506-93506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051506-89891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051507-97121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051507-27571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051507-45296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051507-35859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051507-32903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051508-93749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051508-95630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051508-25707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051508-88135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051508-11195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051509-33202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051509-36044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051509-52527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051509-23503.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051510-44410.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051510-98906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051510-35193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051510-61395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051511-38893.png)
答案
∴AD=BD,
又∵AG ∥BC ,
∴∠GAD= ∠FBD,
∵∠ADG=∠BDF,
∴△ADG≌△BDF,
∴AG=BF;
(2)连接EG。
由(1)△ADG ≌△BDF 可得,GD=FD ,且
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051511-65371.png)
∴EG=EF。
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051511-40166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051511-78102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051512-35040.png)
∴∠EAG+∠ACB=90°,即∠EAG=90°,
∴在
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051512-76882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051512-23168.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051512-65348.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051512-31163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051513-17581.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051513-70563.png)
核心考点
举一反三
(1)试说明BE=DF;
(2)连接AC交EF于点O,延长OC至点M,使OM=OA,连接EM、FM。判断四边形AEMF是什么特殊四边形,并说明你的理由。
![](http://img.shitiku.com.cn/uploads/allimg/20191027/20191027051451-59245.png)
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