阅读下面短文，将文中划线句子译成中文。
　　Some kids in boarding school often like to talk with their roommates. ____ They won’t stop talking until someone comes to stop them. This is the reason why many of them are sleepy in class the next day. Lack of (缺乏) sleep is bad for their health. Growth hormones (生长激素) are very important if one is to grow taller. ____ The body makes the most hormones between 10 p.m. and 2 a.m. While you are asleep. ____ This means that if you don’t get to sleep at the time, you won’t grow taller.

【问题情境】

如图，在正方形ABCD中，点E是线段BG上的动点，AE⊥EF，EF交正方形外角∠DCG的平分线CF于点F．

【探究展示】

（1）如图1，若点E是BC的中点，证明：∠BAE+∠EFC=∠DCF．

（2）如图2，若点E是BC的上的任意一点（B、C除外），∠BAE+∠EFC=∠DCF是否仍然成立？若成立，请予以证明；若不成立，请说明理由．

【拓展延伸】

（3）如图3，若点E是BC延长线（C除外）上的任意一点，求证：AE=EF．