MathNet 1964 — Part 01 Question 13

$ABCD$ is a convex quadrilateral. $A'$ is the foot of the perpendicular from $A$ to the diagonal $BD$, $B'$ is the foot of the perpendicular from $B$ to the diagonal $AC$, and so on. Prove that $A'B'C'D'$ is similar to $ABCD$.