Question 19
Two lines $p$ and $q$ intersect at $C$. The point $C$ divides the line $p$ into two half-lines that, together with one of the half-lines of $q$ with starting point at $C$, form two angles $pCq$ and $qCp$. On the bisector of the angle $pCq$ a point $M$ is chosen such that $MN \parallel p$. The segment $MN$ intersects the line $q$ at a point $D$. Prove that $D$ is the midpoint of the segment $MN$.