In the figure below, given a triangle
ABC, line DEF parallel to AC and line FGM parallel to AB. If S,
S_{1}, S_{2}, and S_{3}, are the areas
of triangles ABC, DBE, FGE, and MGC respectively, prove that: \(\sqrt{S} = \sqrt{S_1} + \sqrt{S_2} + \sqrt{S_3}\).
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