證明：∵四邊形???$ABCD$???為矩形
???$ ∴∠B=∠C=90°，$??????$AB=CD$???
???$ ∵EF⊥ED $???
???$ ∴∠BEF+∠CED=∠FED=90°$???
???$ ∵∠BEF+∠BFE=90°$???
???$ ∴∠BFE=∠CED$???
在???$△BFE$???和???$△CED$???中
???$ \begin{cases}∠B=∠C\\∠BFE=∠CED\\EF=ED\end{cases}$???
???$ ∴△BFE≌△CED(\mathrm {AAS})$???
???$ ∴BE=CD$???
???$ ∴AB=BE，$???
???$ ∴∠BAE=45°$???
???$ ∴AE$???平分???$∠BAD$???
