如图，AB=AC，∠BAC=90°，BD⊥AE于D，CE⊥AE于E，且BD＞CE．求证：BD=EC+ED．

Question

如图，AB=AC，∠BAC=90°，BD⊥AE于D，CE⊥AE于E，且BD＞CE．
求证：BD=EC+ED．

Answer 1

证明：∵∠BAC=90°，CE⊥AE，BD⊥AE，
∴∠ABD+∠BAD=90°，∠BAD+∠DAC=90°，∠ADB=∠AEC=90°．
∴∠ABD=∠DAC．
∵在△ABD和△CAE中

∠ABD＝∠EAC

∠BDA＝∠E

AB＝AC