题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033700-64147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033700-91403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033700-60313.png)
(1)如图
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-87152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-20654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-49916.png)
(2)如图
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-93113.png)
(3)在(2)的情况下,当点D运动到什么位置时,四边形BCFE是菱形?并说明理由。
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-46013.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-43511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-43950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-33646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-94303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-97967.png)
解析
试题分析:(1)①根据等边三角形的性质可得
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-43511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-43950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-33646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-94303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-20654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-99128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033704-89774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033704-49214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033704-99653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033700-60313.png)
(2)证法同(1)
(3)由
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-20654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033704-59553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-97967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033705-74053.png)
解:(1)①∵
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033700-64147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033700-91403.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-43511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-43950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033702-33646.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-94303.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-20654.png)
②四边形BCFE是平行四边形
理由:由①得
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-20654.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-99128.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033704-89774.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033704-49214.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033704-99653.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033700-60313.png)
∴四边形BCFE是平行四边形;
(2)①
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-20654.png)
(3)当点D运动到
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-97967.png)
理由:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033701-20654.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033704-59553.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033703-97967.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033705-74053.png)
∵四边形BCFE是平行四边形
∴四边形BCFE是菱形.
点评:此类问题难度较大,在中考中比较常见,一般在压轴题中出现,需特别注意.
核心考点
试题【是等边三角形,D是射线BC上的一个动点(与点B、C不重合),是以AD为边的等边三角形,过点E作,交射线AC于点F,连结BE.(1)如图,当点D在线段BC上运动时】;主要考察你对相似图形性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033655-90248.png)
A.44° | B.60° | C.67° | D.77° |
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033651-19488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033644-17640.png)
(1)求证:AB⊥AE;
(2)若BC2=AD•AB,求证:四边形ADCE为正方形.
A.![]() ![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() ![]() |
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