The Quadrilateral of Centroids

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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.

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



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

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