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A Relation between Altitudes of Four Triangles

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Let ABC be a triangle and DEF be parallel to AC and FGM be parallel to AB. Let AH, DN, FP, and MQ be altitudes in triangles ABC, DBE, FEG, and MGC respectively. Then with the plus sign when F is outside of ABC and minus when F is inside.

Contributed by: Jay Warendorff (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA

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The statement of the theorem is in Problem 91. Similar Triangles, Altitudes, Parallel.

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