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7922

The Quadrilateral of Centroids

Let ABCD be a quadrilateral and E, F, G and H be the centroids of the triangles ABC, BCD, ACD, and ABD. Then 9×area(EFGH) = area(ABCD). Also EF AD, FG AB, GH BC and EH CD.

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The statement of the theorem is in Problem 98. Quadrilateral Areas, Centroids, Similarity.

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"The Quadrilateral of Centroids" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/TheQuadrilateralOfCentroids/
Contributed by: Jay Warendorff
After work by: Antonio Gutierrez




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