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.
1.) Show that quadrilaterals GFDN and GBMN are trapezoids.
2.) Find the ratios BG : MN, FG : MN, and DN : MN.
3.) Compute the ratio of the area of the quadrilateral GFDN to the area of quadrilateral GBMN.
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