證明 ∶ 如圖，過點?$D$?作?$D M⊥A B $?，?$ D N⊥A C$?，垂足分別為?$ M $?、?$ N$?
即?$ ∠EMD=∠AMD=∠AND=∠FND=90° $?
∵?$AD$?是?$∠BAC$?的平分線
∴?$∠MAD=∠NAD$?
在?$△AMD$?和?$△AND $?中
?$\begin {cases}{∠M A D=∠N A D}\\{∠A M D=∠A N D }\\{A D=A D}\end {cases}$?
∴?$△AMD≌△AND(\mathrm {AAS}) $?
∴?$D M=D N$?
在?$△EMD$?和?$△FND$?中?$ $?
?$\begin {cases}{∠E M D=∠F N D}\\{∠M E D=∠N F D}\\{ D M=D N}\end {cases}$?
∴?$△EMD≌△FND(\mathrm {AAS}) $?
∴?$DE=DF$?
