In the figure below, given a triangle
ABC, an altitude AH = h, line DEF parallel to AC and line FGM
parallel to AB. If h1, h2, and h3
are perpendicular to BC respectively, prove that: h = h1
+ h2 + h3.
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. SIMILAR TRIANGLES:
Corresponding segments of similar triangles are in proportion.
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