Centroid

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The centroid of a triangle is the point of intersection of the medians of the triangle. The centroid has the special property that, for each median, the distance from a vertex to the centroid is twice that of the centroid to the side. Also, the three medians of a triangle divide it into six regions of equal area. The centroid is the center of mass of the triangle.

(pictures needed) (proofs of these properties anyone?) (example problems?)