如图,AB=CD,AE⊥BC,DF⊥BC,垂足分别为E,F,CE=BF.求证AE=DF
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如图,AB=CD,AE⊥BC,DF⊥BC,垂足分别为E,F,CE=BF.求证AE=DF
∵ae⊥bc,df⊥bc
∴∠dfc=∠aeb=90°
∵ce=cf+ef,bf=be+fe,ce=bf
∴cf=be
又∵ab=cd
∴△abe≌△cdf(HL)
∴ae=df
∴∠dfc=∠aeb=90°
∵ce=cf+ef,bf=be+fe,ce=bf
∴cf=be
又∵ab=cd
∴△abe≌△cdf(HL)
∴ae=df
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