题目

如图所示,在△ABC中AB=AC,BD⊥AC于D,CE⊥AB于E,BD,CE交于F,说明AF平分∠BAC

提问时间：2021-02-08

答案

证明：
∵∠AEC = ∠ADB = 90 °
∠BAC为公共角
AB = AC
∴ △ADB≌△AEC 且为直角三角形
∵AB = AC
∴∠ABC = ∠ACB
又∵∠ABD = ∠ACE
=>∠DBC = ∠ECB
=>BF = CF
=>∠BAF = ∠CAF
即证：AF平分∠BAC