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_其他解答

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

人气：253 ℃　时间：2019-10-23 05:22:40

解答

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