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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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