$DF=DE$
理由：
如图，连接$AD$
$\because AB=AC$，$\angle BAC=90°$，$D$是$BC$的中点
$\therefore AD=BD=\dfrac {1} {2}BC$，$\angle B=\angle C=45°$，$\angle 1=\angle 2=45°$，$AD\bot BC$
$\therefore \angle B=\angle 2$，$\angle ADB=90°$
$\therefore \angle 5+\angle 3=90°$
$\because \angle EDF$是直角
$\therefore \angle 3+\angle 4=90°$
$\therefore \angle 5=\angle 4$
$\therefore \triangle BDE≌\triangle ADF\left ( {ASA} \right )$
$\therefore DE=DF$.
