解?$ ∶ $?在?$Rt△ABF $?和?$Rt△AGF{中}$?
?$\begin {cases}{A G=A B}\\{A F=A F}\end {cases}$?
∴?$Rt△ABF≌ Rt△AGF(\mathrm {HL})$?
∴?$∠BAF=∠GAF$?，?$AG=AB=AD$?
在?$Rt△ AGE$?和?$Rt△ADE$?中
?$\begin {cases}{A G=A D}\\{A E=A E}\end {cases}$?
∴?$Rt \triangle AGE≌ Rt \triangle ADE(\mathrm {HL})$?
∴?$∠GAE=∠DAE$?
∴?$∠EAF=∠GAF+∠GAE=\frac {1}{2}(∠BAG+∠GAD)=45°$?
