Suppose ABCD and AB'C'D' are two squares in t…

Suppose ABCD and AB’C’D’ are two squares in the plane that a) have vertex A in common, b) have the same orientation of the vertices, and c) lie outside one another. Let P be the intersection of the diagonals AC and BD; let Q be the intersection of the diagonals AC’ and B’D’ ; let R be the midpoint of the segment BD’ , and let S be the midpoint of the diagonal B’D. Prove that PQRS is a square by first showing that segment PS transforms into PR by a rotation through 90◦ . (Do not denote complex numbers corresponding to P, etc., by P, etc.; use for instance corresponding small letters.)