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In the figure below, given an
equilateral triangle ABC, D is an interior point. If
AD = d, BD = e, CD = f, and
 ,
prove that the area S of triangle ABC is:
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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."
USE
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Congruence of Triangles SAS
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Congruence of triangles SSS
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Heron's formula of area of a triangle
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Formula of the area of an equilateral triangle:
 ,
where s is any side.
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