Question 6
In a convex quadrilateral $ABCD$, $|AB| = |BC| = |CD|$. Let furthermore, for the intersection $P$ of its diagonals, $|\angle APD| \lt 90^\circ$. Let $R$ and $S$ be reflections of $A$ and $D$ with respect to $BD$ and $AC$, respectively. Prove that the lines $BC$ and $RS$ are parallel.