?$ (1)$?證明：∵?$AD$?平分?$∠BAC，$??$∠C = 90°，$??$DE\perp AB$?
∴?$DC = DE$?
?$ $?在?$Rt\triangle DCF $?和?$Rt\triangle DEB$?中
?$ \begin {cases}DC = DE\\DF=DB\end {cases}$?
∴?$Rt\triangle DCF≌ Rt\triangle DEB(\mathrm {HL})$?
∴?$CF = EB$?
?$ (2)$?解：?$AE=AF + BE$?
理由：∵?$AD$?平分?$∠BAC，$?∴?$∠CAD=∠EAD$?
在?$Rt△ACD$?和?$Rt△AED$?中
?$\begin {cases}{DC=DE}\\{AD=AD}\end {cases}$?
∴?$\triangle ACD≌\triangle AED(\mathrm {HL})$?
∴?$AC = AE$?
又∵?$AC=AF + CF，$?且?$CF = EB$?
∴?$AE=AF + BE$?
