(1) 如图1,在正方形ABCD中,点E,F分别在边BC,CD上,AE,BF交于点O,∠AOF=90°.求证:BE=CF.
![](https://media.youtike.com//ques/201210/26/808a8f1c-f464-4df9-b41b-9a8e94749031/image001.png)
(2) 如图2,在正方形ABCD中,点E,H,F,G分别在边AB,BC,CD,DA上,EF,GH交于点O,∠FOH=90°, EF=4.求GH的长.
![](https://media.youtike.com//ques/201210/26/808a8f1c-f464-4df9-b41b-9a8e94749031/image002.png)
(3) 已知点E,H,F,G分别在矩形ABCD的边AB,BC,CD,DA上,EF,GH交于点O,∠FOH=90°,EF=4. 直接写出下列两题的答案:
①如图3,矩形ABCD由2个全等的正方形组成,求GH的长;
![](https://media.youtike.com//ques/201210/26/808a8f1c-f464-4df9-b41b-9a8e94749031/image003.png)
②如图4,矩形ABCD由n个全等的正方形组成,求GH的长(用n的代数式表示).![](https://media.youtike.com//ques/201210/26/808a8f1c-f464-4df9-b41b-9a8e94749031/image004.png)