Question

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

Answer 1

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