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Geometry Problem 1124: Triangle, Median, Two Squares, Area. Level: High School, SAT Prep, Honors Geometry, College, Math Education

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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.
 

Infographic Geometry problem 1124 Triangle, Median, Two Squares, Area
 

 

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Last updated: Jun 19, 2015 by Antonio Gutierrez.