The Quadrilateral of Centroids
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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
Snapshots
Details
The statement of the theorem is in Problem 98. Quadrilateral Areas, Centroids, Similarity.
Permanent Citation
"The Quadrilateral of Centroids"
http://demonstrations.wolfram.com/TheQuadrilateralOfCentroids/
Wolfram Demonstrations Project
Published: March 7 2011