如图,AB=CD,AE⊥BC,DF⊥BC,CE=BF.求证:AE=DF.

问题描述:

如图,AB=CD,AE⊥BC,DF⊥BC,CE=BF.求证:AE=DF.

证明:∵AE⊥BC,DF⊥BC,
∴∠DFC=∠AEB=90°,
又∵CE=BF,
∴CE-EF=BF-EF,即CF=BE,
∵AB=CD,
∴Rt△DFC≌Rt△AEB(HL),
∴AE=DF.