Question 19
Let $A B C D E$ be a convex pentagon with the properties
$$
\overline{A B}=\overline{B C}=\overline{C D}, \angle B A E=\angle D C B \text{ and } \angle E D C=\angle C B A .
$$
Prove that the perpendicular from $E$ to $B C$ passes through the intersection point of $A C$ and $B D$.
$$
\overline{A B}=\overline{B C}=\overline{C D}, \angle B A E=\angle D C B \text{ and } \angle E D C=\angle C B A .
$$
Prove that the perpendicular from $E$ to $B C$ passes through the intersection point of $A C$ and $B D$.