KöMaL 2026 B5543

Let $e$ and $f$ be the opposite side of a rectangular pool table, and let $A$ and $B$ be two interior points. Prove that if a billiard ball travels from $A$ to be $B$ such that it bounces twice on side $e$ and bounces twice on side $f$ (and does not bounce on the other two sides), then it will travel through the midpoint of line segment $AB$.