Consider the diagram below, which displays a quadrilateral ABCD of area S. The triangles ABC, BCD, ACD, and ABD have centroids E, F, G, and H respectively.
Let S_{1} be the area of the quadrilateral EFGH. It can be proven that (1) EF, FG, GH, and EH are parallel to AD, AB, BC, and CD respectively, and (2) S = 9S_{1}.
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Geometric shapes Centroids, areas, similarity A world of wonders
