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In the figure below, given a triangle
ABC, line DEF parallel to AC and line FGM parallel to AB. If S,
S1, S2, and S3, are the areas
of triangles ABC, DBE, FGE, and MGC respectively, prove that:
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FACTS AND HINTS:
Geometry problem solving is one of the most
challenging skills for students to learn. When a
problem requires auxiliary construction, the
difficulty of the problem increases drastically,
perhaps because deciding which construction to
make is an ill-structured problem. By
“construction,” we mean adding geometric figures
(points, lines, planes) to a problem figure that
wasn’t mentioned as "given."
1. COMPARING AREAS OF SIMILAR
TRIANGLES:
Proposition: The areas of similar triangles are to each
other as the squares of any two corresponding segments.
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