Question 101
The internal bisector of angle $\angle B$ of triangle $ABC$ where $\angle A \gt 90^\circ$, intersects side $AC$ at point $D$. Points $A'$ and $F$ are chosen on side $BC$ such that $AB = A'B$ and $\angle AFB = 2\angle ADB$. Points $E$ and $G$ are on the line $BC$ such that $AD = DE$, $EF = FG$, $E \neq A'$ and $G \neq E$. Prove that lines $DF$ and $AG$ are parallel.
(Khulan Tumenbayar)
(Khulan Tumenbayar)