Question 189
In the convex pentagon $ABCDE$, $|\angle CBA| = |\angle BAE| = |\angle AED|$ holds. On the sides $AB$ and $AE$, there are points $P$ and $Q$, respectively, such that $|AP| = |BC| = |QE|$ and $|AQ| = |BP| = |DE|$. Prove that $CD \parallel PQ$. (Patrik Bak)