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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.
Contributed by:
Jay Warendorff
After work by:
Antonio Gutierrez
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The statement of the theorem is in
Problem 98. Quadrilateral Areas, Centroids, Similarity
.
RELATED LINKS
Quadrilateral
(
Wolfram
MathWorld
)
Triangle Centroid
(
Wolfram
MathWorld
)
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"
The Quadrilateral of Centroids
" from
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http://demonstrations.wolfram.com/TheQuadrilateralOfCentroids/
Contributed by:
Jay Warendorff
After work by:
Antonio Gutierrez
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