证明:证法一:∵四边形ABCD是平行四边形,∴AB∥CD,AB=CD.∴∠BAE=∠DCF.∵AE=CF,∴△ABE≌△CDF.∴BE=DF.证法二:∵四边形ABCD是平行四边形,∴AD∥BC,AD=BC.∴∠DAF=∠BCE.∵AE=CF,∴AF=AE+EF=CF+EF=CE.∴△ADF≌△CBE.∴BE=DF.
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