Problem 97.
Similar Triangles, Areas.
Level: High School, SAT Prep, College

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:
.
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FACTS AND HINTS:

1. COMPARING AREAS OF SIMILAR
TRIANGLES:
Proposition: The areas of similar triangles are to each
other as the squares of any two corresponding segments.