Question

如图一,四边形ABCD是正方形,点E是BC延长线上的一点,

Answer 1

∵ABCD是正方形,∴∠DCG＝90°,又CF平分∠DCG,∴∠ECF＝∠DCF＝45°.

∵ABCD是正方形,∴∠ACD＝45°,∴∠ACF＝∠ACD＋∠DCF＝45°＋45°＝90°.

∵∠AEF＝90°、∠ACF＝90°,∴A、C、E、F共圆,∴∠EAF＝∠ECF＝45°.

∵∠AEF＝90°、∠EAF＝45°,∴∠AFE＝45°,∴∠EAF＝∠AFE,∴AE＝EF.