Problem 91. Similar Triangles, Altitude, Parallel,
Perpendicular.
Level: High School, College

In the figure below, given a triangle
ABC, an altitude AH = h, line DEF parallel to AC and line FGM
parallel to AB. If h_{1}, h_{2}, and h_{3}
are perpendicular to BC respectively, prove that: h = h_{1}
+ h_{2} + h_{3}.
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FACTS AND HINTS:

1. SIMILAR TRIANGLES:
Proposition:
Corresponding segments of similar triangles are in proportion.