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