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A Relation between the Areas of Four Triangles

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Let ABC be a triangle. Let DEF be parallel to AC with D on AB and E on BC. Let FGH be parallel to AB with G on BC and H on AC. 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 97. Similar Triangles, Areas.

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