题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033730-94010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033730-11179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033730-28163.png)
(1)如图①,当
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033731-33587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033731-62468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033731-76662.png)
(2)如图②,当
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033731-33587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033732-58921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033732-64572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033732-64984.png)
(3)如图③,当
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033732-56839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033732-58921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033732-64572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033732-64984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-16176.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-92513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033730-11179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033730-28163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033731-33587.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-52017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033731-62468.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-37805.png)
根据含30°角的直角三角形的性质可得
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-63775.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-84369.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-52174.png)
解析
试题分析:(1)在四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-92513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033730-11179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033730-28163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033731-33587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-52017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033731-62468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-37805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-63775.png)
(2)过
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033735-96099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033735-67604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033735-28863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033735-86607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033736-29264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033736-92693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033736-69135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033736-37193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033737-87117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033737-17883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033737-51895.png)
(3)解法同(2).
解:(1)在四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-92513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033737-30640.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-52017.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033738-56860.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033733-37805.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-63775.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-84369.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-84369.png)
证明如下:如图,过
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033735-96099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033735-67604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033735-28863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033738-74774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033738-24650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033738-58040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033739-92937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033735-86607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033736-29264.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033736-92693.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033736-69135.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033736-37193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033737-87117.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033737-17883.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033739-48237.png)
由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033737-51895.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-84369.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033734-52174.png)
点评:全等三角形的判定和性质是初中数学的重点,贯穿于整个初中数学的学习,是中考中比较常见的知识点,一般难度不大,需熟练掌握.
核心考点
试题【在四边形中,对角线平分.(1)如图①,当,时,求证:;(2)如图②,当,与互补时,线段有怎样的数量关系?写出你的猜想,并给予证明;(3)如图③,当,与互补时,线】;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/20191103/20191103033725-90276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033726-32988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033726-25322.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033720-91331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033720-99733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033720-92113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033721-79080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033721-84529.jpg)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033714-34080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033714-34762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033708-13776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033708-75448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033709-20015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033709-31893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033709-19565.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033710-92356.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103033710-54270.png)
![](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)
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