?$ (1)$?證明：∵?$AB⊥AC，$??$AD⊥AE，$?
∴?$∠BAC=∠DAE=90°$?
∴?$∠BAC - ∠EAB=∠DAE - ∠EAB，$?即?$∠CAE=∠BAD$?
在?$?ABD$?和?$?ACE$?中
?$ \begin {cases}{∠ABD=∠ACE}\\{AB=AC}\\{∠BAD=∠CAE}\end {cases}$?
∴?$?ABD≌?ACE(AS A)$?
∴?$BD=CE$?
?$(2)$?解：?$BD⊥CE，$?理由：設(shè)?$BD$?與?$CE$?交于點(diǎn)?$F$?
由?$(1)$?知?$?ABD≌?ACE，$?∴?$∠ADB=∠AEC$?
∵?$∠AEC+∠AEF=180°，$?∴?$∠ADB+∠AEF=180°$?
∵?$∠DAE=90°$?
∴?$∠DEF=360°-(∠ADB+∠AEF)-∠DAE=90°$?
∴?$BD⊥CE$?
