证明:$\because AB// CD,$$AE// CF,$
$\therefore ∠ B = ∠ D,$$∠ AEB = ∠ CFD。$
$\because BF = DE,$
$\therefore BE = DF。$
在$△ ABE$和$△ CDF$中,
$\begin{cases} ∠ B = ∠ D, \\ BE = DF, \\ ∠ AEB = ∠ CFD, \end{cases}$
$\therefore △ ABE ≌ △ CDF(\mathrm{ASA}),$
$\therefore AB = CD。$