△ABC中,AB=AC点D是BC中点DF⊥AC于点F,E是DF中点,求证AE⊥BF
问题描述：
△ABC中,AB=AC点D是BC中点DF⊥AC于点F,E是DF中点,求证AE⊥BF
答
取CF的中点G,连接DG,DA∵D是BC的中点,AB = AC∴AD⊥BC∵DF⊥AC∴∠DAF =∠FDC∴△DAF∽△DFC∴AF：DF = DF：CF∵E是DF的中点,G是FC的中点∴AF：DF = EF：FG∴△AFE∽△DFG∴∠FAE = ∠FDG∵G是FC的中点∴在△CBF中,D...