證明：在?$\triangle ABE$?和?$\triangle ACE$?中
?$ \begin {cases}AB = AC\\BE = CE\\AE = AE\end {cases}$?
∴?$\triangle ABE≌\triangle ACE(\mathrm {SSS})$?
∴?$∠BAD=∠CAD$?
?$ $?在?$\triangle ABD$?和?$\triangle ACD$?中
?$ \begin {cases}AB = AC\\∠BAD=∠CAD\\AD = AD\end {cases}$?
∴?$\triangle ABD≌\triangle ACD(S AS)$?
∴?$∠ADB=∠ADC$?
?$ $?又?$∠ADB+∠ADC = 180°$?
∴?$∠ADB=∠ADC = 90°，$?即?$AD\perp BC$?
