證明：∵點?$D$?為?$BC$?的中點，∴?$BD = CD$?
又∵?$DE\perp AB，$??$DF\perp AC$?
∴?$∠BED=∠CF D = 90°$?
?$ $?在?$Rt\triangle BED$?和?$Rt\triangle CF D$?中
?$\begin {cases}BD = CD\\DE = DF\end {cases}$?
∴?$Rt\triangle BED≌ Rt\triangle CF D(\mathrm {HL})$?
∴?$∠B=∠C$?
∴?$AB = AC$?
∴?$\triangle ABC$?為等腰三角形
