如图所示,在Rt△ABC中,AB=AC,∠BAC=90°,过A作一条直线AN,BD⊥AN于D,CE⊥AN于E,求证：DE=BD-CE

Question

如图所示,在Rt△ABC中,AB=AC,∠BAC=90°,过A作一条直线AN,BD⊥AN于D,CE⊥AN于E,求证：DE=BD-CE

Answer 1

∵∠BAD+∠ABD=∠BAD+∠CAE=90°
∴∠ABD=∠CAE
∵∠ADB=∠AEC=90°
AB=AC
∴RT△ABD≌RT△CAE
∴CE=AD,BD=AE
∵DE=AE-AD
∴DE=BD-CE