In square ABCD, E and F are the midpoints of BC and CD, respectively. Line segments BF and AE intersect at G. Let M be the midpoint of AB, and let N be the intersection of AE and DM.
(a) Show that quadrilaterals GFDN and GBMN are trapezoids.
(b) Find the ratios BG : MN, FG : MN, and DN : MN.
(c) Compute the ratio of the area of the quadrilateral GFDN to the area of quadrilateral GBMN.