Question 113
A triangle $A B C$ is given. Let $D$ and $E$ be points lying on the rays $C A$ and $C B$, respectively, but not on the sides of triangle $A B C$, such that $|A D|=|B E|=|A B|$. Let $F$ be the intersection of the line through the point $E$ parallel to $A C$ and the line through the point $D$ parallel to $B C$. Denote the intersection of the lines $A E$ and $B D$ by $G$. Prove that the line $F G$ is the bisector of the angle $\angle E F D$.