题目
题型:不详难度:来源:
在如图所示的一张矩形纸片
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-89946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-93400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-46210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-29837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-56980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002212-71672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002212-41845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002212-39587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002212-12965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002212-32570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002212-78510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-89617.png)
小题1:(1)求证:四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-28564.png)
小题2:(2)过
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002212-41845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-98886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-39903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-73203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-82482.png)
小题3:(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-61266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-80636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-25256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-80636.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-86393.png)
小题1:(1)连结
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-56980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-39903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-67015.png)
当顶点
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-46210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-29837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-56980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-39903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-27902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-41219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-72373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002211-89946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002215-31942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002215-74983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002215-68367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002215-41357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002216-88063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-28564.png)
小题2:(2)证明:过
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002212-41845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-98886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-39903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-73203.png)
由作法,
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002216-91433.png)
由(1)知:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002216-31304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002216-81463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002217-37643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002217-51142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002217-38444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-72373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-28564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002217-99316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002218-82988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002218-68032.png)
小题3:(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002214-72373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002213-28564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002218-12281.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002218-15558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002219-46542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002219-91898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002219-34122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002219-45429.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002220-31802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002220-97326.png)
由①、②得:
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002220-27911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002220-83068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002220-77962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002221-43167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103002221-69462.png)
解析
核心考点
试题【(本小题满分14分)在如图所示的一张矩形纸片()中,将纸片折叠一次,使点与重合,再展开,折痕交边于,交边于,分别连结和.小题1:(1)求证:四边形是菱形;小题2】;主要考察你对相似图形等知识点的理解。[详细]
举一反三
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?
![](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)
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