△ABC中,AB=AC点D是BC中点DF⊥AC于点F,E是DF中点,求证AE⊥BF

△ABC中,AB=AC点D是BC中点DF⊥AC于点F,E是DF中点,求证AE⊥BF
△ABC中,AB=AC点D是BC中点DF⊥AC于点F,E是DF中点,求证AE⊥BF

△ABC中,AB=AC点D是BC中点DF⊥AC于点F,E是DF中点,求证AE⊥BF
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,DG//BF
∴∠GDF = ∠BFD
∴∠FAE = ∠BFD
∵AF⊥DF
∴∠FAE ∠FEA = 90°
∴∠BFD ∠FEA = 90°
∴AE⊥BF
（下次先搜索一下,感谢古树上的月）