已知AE⊥AB,AF⊥AC,AE=AB,AF=AC.试证明:(1)EC=BF;(2)EC⊥BF
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已知AE⊥AB,AF⊥AC,AE=AB,AF=AC.试证明:(1)EC=BF;(2)EC⊥BF
已知AE⊥AB,AF⊥AC,AE=AB,AF=AC.试证明:(1)EC=BF;(2)EC⊥BF
已知AE⊥AB,AF⊥AC,AE=AB,AF=AC.试证明:(1)EC=BF;(2)EC⊥BF
画图:
(1)
∵AE=AB,AF=AC
而∠EAC = 90°+∠BAC,∠BAF= 90°+∠BAC,即∠EAC = ∠BAF
∴△AEC ≌△ABF(SAS)
∴EC = BF
(2)
设BF角CE于O
∵△AEC ≌△ABF (已证)
∴∠AFB = ∠ACE
而AF⊥AC,AF=AC
∴△ACF是直角等腰三角形,∠AFC = ∠ACF = 45°
又∵在△CFO中,∠OFC = 45° -∠AFB,∠OCF = 45° +∠AFB
∴∠OFC 与∠OCF互余, ∠COF = 90°
∴EC⊥BF
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