情境·观察:
将矩形ABCD纸片沿对角线AC剪开,得到△ABC和△
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/20140823033158429541.png)
,如图1所示,将△
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/20140823033158429541.png)
的顶点
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/20140823033158460328.png)
与点A重合,并绕点A按逆时针方向旋转,使点D,A(
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/20140823033158460328.png)
),B在同一条直线上,如图2所示,观察图2可知:旋转角
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/20140823033158491510.png)
=
° ,与BC相等的线段是
。
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/2014082303315852211348.png)
问题·探究:
如图3,△ABC中,AG⊥BC于点G,以A为直角顶点,分别以AB、AC为直角边,向△ABC外作等腰直角△ABE和等腰直角△ACF,过点E、F作射线GA的垂线,垂足分别为P、Q,试探究EP与FQ之间的数量关系,并证明你的结论。
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/2014082303315853823527.png)
关系·拓展:
如图4,已知正方形ABCD,P为边BC上任意一点,连结AP,把AP绕点P顺时针方向旋转90°,点A对应点为点
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/20140823033158460328.png)
,连接
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/20140823033158569436.png)
,求
![](http://thumb.1010pic.com/pic2/upload/papers//20140823/20140823033158585578.png)
的度数。