题目

如图①,在三角形ABC中,∠BAC=90°,AB=AC,AE是直线,点B、C在AE的异侧,BD⊥AE于点D,CE⊥AE于点E
请说明BD=DE+CE

提问时间：2021-01-05

答案

证明：∵∠BAD+∠ABD = 90°
∠BAD+∠CAE = 90°
∴∠ABD = ∠CAE
∵∠ADB = ∠CEA = 90°
AB = AC
∴△ABD≌△CAE
∴CE = AD BD = AE
∵AE = AD+DE
∴BD = DE+CE