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The Midpoints of Two Cevians

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A cevian is a line drawn from a vertex of a triangle to the opposite side.

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Let ABC be a triangle and let M and N be the midpoints of the cevians BB' and CC'. Then the area of the quadrilateral BC'B'C is 4 times the area of AMN.

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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 90. Quadrilateral and Triangle Areas, Midpoints.

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