The figure below shows a triangle
ABC with the median BM. AMDE and BMFG are squares so that MF meets
BC at H and DF meets AC and BC at Q and P, respectively. If S1,
S2, S3, and S4 are the areas of
triangles BHM, FHP, CPQ, and DMQ, respectively, prove that S1 +
S3 = S2 + S4.
![Honors Geometry problem 1124 Triangle, Median, Two Squares, Area Infographic Geometry problem 1124 Triangle, Median, Two Squares, Area](p1124-triangle-median-square-area-math.gif)
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