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Centroid is the Balance Point of a Triangle

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Need to prove that the centroid is the balance point of a triangle using only GEOMETRY with no vector addition allowed and I can't use the "equal areas" argument as far as the 6 triangles that are made with the medians. Thanks much

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The expert proves that the centroid is the balance point of a triangle.

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The proof is attached below. It can also be found at

http://members.aol.com/rmp605/Geometry/pow970714.html

The basic idea is to construct the triangle from a parallelogram ...

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