PABCDE is a pyramid with ABCDE a convex pentagon. A plane meets the edges PA, PB, PC, PD, PE in points A', B', C', D', E' distinct from A, B, C, D, E and P. For each of the quadrilaterals ABB'A', BCC'B, CDD'C', DEE'D', EAA'E' take the intersection of the diagonals. Show that the five intersections are coplanar.