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Relating the areas of regions determined by joining midpoints of two sides of a convex quadrilateral to...

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up vote 0 down vote favorite 1 I have tried solve the following problem, but I can not see how to approach it: In the figure, $ABCD$ is an arbitrary convex quadrilateral, $M$ and $N$ are, respectively, the middle points of $overline{AB}$ and $overline{CD}$, and $S,S_1,S_2$ are the area of the shaded regions. Prove that $$S=S_1+S_2$$ Any hints are welcome! euclidean-geometry problem-solving area share | cite | improve this question edited Jun 12 at 18:58 asked Jun 12 at 18:33 DiegoMath ...