如图,AD⊥BC,CE⊥AB,垂足分别是D.E,AD交CE于点F,AD=EC.求证AE=CD

如图,AD⊥BC,CE⊥AB,垂足分别是D.E,AD交CE于点F,AD=EC.求证AE=CD
如图,AD⊥BC,CE⊥AB,垂足分别是D.E,AD交CE于点F,AD=EC.求证AE=CD

如图,AD⊥BC,CE⊥AB,垂足分别是D.E,AD交CE于点F,AD=EC.求证AE=CD
证明：∵AD⊥BC,CE⊥AB
∴△AEC和△CAD是直角三角形
∵在RT△AEC和RT△CAD中
AD=AE,AC=CA
∴RT△AEC≌RT△CAD
∴AE=CD