题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075448-78663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075448-30810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075448-95688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075448-96500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075448-68372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075449-40894.png)
求证:△
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075449-54196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075449-48476.png)
![]() |
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075448-95688.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075450-78873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075450-22092.png)
∠
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075450-78093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075451-30836.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075451-54630.png)
∴∠
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075451-99352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075451-34744.png)
由等角的补角相等
∴∠
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075451-90013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075452-76369.png)
∴△
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075449-54196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075452-63372.png)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075429-60390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075429-24861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075429-26824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075429-69417.png)
⑴连结
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075429-92383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075430-86694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075430-53914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075430-35171.png)
▲ ;过
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075430-66120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075430-36860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075431-76392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075431-13170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075431-12256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075432-89672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075432-47510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075432-56136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075432-97803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075433-24476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075433-77120.png)
⑵在图1中,若将三个正方形“退化”为正三角形,得到图3,同学们可以探究△
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075433-37282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075433-97794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075434-17841.png)
⑶为了研究问题的需要,将图1中的
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075434-38815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075434-42890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075434-42890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075429-24861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075434-35618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075433-37282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075433-97794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075433-37282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075434-65228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075435-41534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075435-24518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075435-41534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075435-44804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075434-42890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075436-50555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075430-66120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075435-24518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075435-41534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075436-69635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075436-95194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075436-65416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075436-86459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075437-64611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075422-12263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075423-78263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075423-51720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075423-36322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075419-32808.png)
求证:∠ACD=∠ADC.
问题1:如图1,若∠ACB=90°,AC=
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075413-16648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075413-29113.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075413-16648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075413-29113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075413-47299.png)
问题2:如图2,若∠ACB为钝角,且AB>AC,BD>DC.
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075414-38461.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075414-53155.png)
(2)若点E在AD上,且DE=DB,延长CE交AB于点F,求∠BFC的度数.
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075409-97994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075409-60993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103075409-65817.png)
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