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Centroid is the Balance Point of a Triangle

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 proof is attached below. It can also be found at
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<br>http://members.aol.com/rmp605/Geometry/pow970714.html
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<br>The basic idea is to construct the triangle from a ...

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