证明:∵$AB//CD,$$AE//CF$
∴$∠B = ∠D,$$∠AEB = ∠CF D$
又$ BF = DE$
∴$BF + FE = DE + FE,$即$ BE = DF$
在$ \triangle ABE $和$ \triangle CDF $中
$\begin {cases}∠B=∠D\\BE = DF\\∠AEB=∠CF D\end {cases}$
∴$\triangle ABE≌\triangle CDF(AS A)$
∴$AB = CD$