ILL 1979 Problem 22

Consider two quadrilaterals $ABCD$ and $A'B'C'D'$ in an affine Euclidian plane such that $AB = A'B', BC = B'C', CD = C'D'$ , and $DA = D'A'$ . Prove that the following two statements are true:(a) If the diagonals $BD$ and $AC$ are mutually perpendicular, then the diagonals $B'D'$ and $A'C'$ are also mutually perpendicular.(b) If the perpendicular bisector of $BD$ intersects $AC$ at $M$ , and that of $B'D'$ intersects $A'C'$ at $M'$ , then $\frac{\overline{MA}}{\overline{MC}}=\frac{\overline{M'A'}}{\overline{M'C'}}$ (if $MC = 0$ then $M'C' = 0$ ).