题目
题型:不详难度:来源:
操作:如图1,将正方形纸片折叠,使顶点A落在边CD上的点P处(点P与C、D不重合),折痕为EF,折叠后AB边落在PQ的位置,PQ与BC交于点G.
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-90516.png)
探究:小题1:(1)观察操作结果,找到一个与△DEP相似的三角形,并证明你的结论;
小题2:(2)当点P位于CD中点时,你找到的三角形与△DEP周长的比是多少?
答案
小题1:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-48754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-12535.png)
证明:∵四边形ABCD是正方形,
∴∠A=∠C=∠D=
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-22202.png)
由折叠知 ∠EP
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002200-97041.png)
∴∠PED+∠DPE=90°,∠DPE+∠CPG=90°.
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002200-38576.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-48754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-12535.png)
小题2:(2)设ED=x,则AE=
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002200-43543.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002200-44219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002200-43543.png)
∵点P是CD中点,∴DP=1.
∵∠D=90°,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002201-27138.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002201-75575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002201-35682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002201-95470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002202-53980.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-48754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-12535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002202-58245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-48754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002159-12535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002202-37500.png)
解析
核心考点
试题【已知正方形纸片ABCD的边长为2.操作:如图1,将正方形纸片折叠,使顶点A落在边CD上的点P处(点P与C、D不重合),折痕为EF,折叠后AB边落在PQ的位置,P】;主要考察你对相似图形等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002153-14941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002153-45881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002139-70394.png)
小题1:(1)求抛物线的解析式;
小题2:(2)在抛物线上求点M,使△MOB的面积是△AOB面积的3倍;
小题3:(3)连结OA,AB,在x轴下方的抛物线上是否存在点N,使△OBN与△OAB相似?若存在,求出N点的坐标;若不存在,说明理由.
小题1:(1)将图1中△A1B1C绕点C顺时针旋转45°得图2,点
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002126-86692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002126-49913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002126-78350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002127-31705.png)
小题2:(2)在图2中,若AP1=
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002127-87751.png)
小题3:(3)将图2中△
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002127-81263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002127-46556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002127-94298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002128-90570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002128-80666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002110-62650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002111-46300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002111-23440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002111-82743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002111-94219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002111-77988.png)
点
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002112-69112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002112-76949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002111-23440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002112-95069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002112-24887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002111-82743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002113-11822.png)
小题1:(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002113-16070.png)
小题2:(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002113-52980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002113-55482.png)
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