Consider a convex quadrilateral A B C D. Let rays B A and C D intersect at E, rays D A and C B intersect at F, and the diagonals A C and B D intersect at G. It is given that the triangles D B F and D B E have the same area.
(a) Prove that E F and B D are parallel.
(b) Prove that G is the midpoint of BD.
(c)Given that the area of triangle A B D is 4 and the area of triangle C B D is 6, compute the area of triangle E F G.