Problem #NZO-000005

Problem

Let $A B C$ be an isosceles triangle with $A B = A C$ . Point $D$ lies on side $A C$ such that $B D$ is the angle bisector of $∠ A B C$ . Point $E$ lies on side $B C$ between $B$ and $C$ such that $B E = C D$ . Prove that $D E$ is parallel to $A B$ .

To see the solution register and get verified.