Question 83
Let $ABC$ be an acute-angled triangle such that $m(\angle ACB) \neq 45^\circ$. The points $M$ and $N$ are the feet of the altitudes, drawn from the vertices $A$ and $B$ respectively. The points $P$ and $Q$ lie on the half-straight lines $MA$ and $NB$ respectively so that $MP = MB$ and $NQ = NA$. Prove that the straight lines $PQ$ and $MN$ are parallel.