Tools: In this problem you can use any theorem or homework problem proved in the course.

Given a quadrilateral ABCD, let M and N be the midpoints of AB and CD. Let X and Y be the midpoints of the diagonals BD and AC.

(a) Assuming that AD is not parallel to BC, prove that the quadrilateral MXNY is a parallelogram.

(b) Describe and prove what is the nature of the figure MXNY when AD is parallel to BC.