证明:$\because DE\perp BC,$$DF\perp AC,$$\therefore \angle DEC=\angle DFC = 90^{\circ}.$
又$\because \angle ACB = 90^{\circ},$$\therefore$四边形$CFDE$是矩形.
$\because CD$平分$\angle ACB,$$DE\perp BC,$$DF\perp AC,$
$\therefore DE = DF.$
$\therefore$矩形$CFDE$是正方形.