题目

 One morning, I was waiting at the bus stop, worried about being late for school. There were many people __61______(wait) at the bus stop, and some of them looked very anxious and ____62______ (disappoint). When the bus finally came, we all hurried on board. I got a place next ___63__ the window, ___64_______ I had a good view of the sidewalk. A boy on a bike cahght my attention. He was riding beside the bus and waving his arms. I heard a passenger behind me shouting to the driver, but he refused to stop __65_____we reached the next stop. Still, the boy kept riding. He was carrying som如图，正方形ABCD的边长为1，点F在线段CD上运动，AE平分∠BAF交BC边于点E．（1）过A作AG⊥AF，交CB延长线于点G，求证：①AG=AF，②AF=DF+BE；（2）延长AF交BC延长线于点H，若AE=EH，求此时DF的长．