解:$BE=DF,$理由如下:
$\because$ 四边形$ABCD$是平行四边形,
$\therefore AB=CD,$$AB// CD,$
$\therefore ∠ BAE=∠ DCF,$
$\because BE⊥ AC,$$DF⊥ AC,$
$\therefore ∠ AEB=∠ CFD=90°,$
在$△ AEB$和$△ CFD$中,
$\begin{cases}∠ AEB=∠ CFD \\∠ BAE=∠ DCF \\AB=CD\end{cases}$
$\therefore △ AEB≌△ CFD(\mathrm{AAS}),$
$\therefore BE=DF。$