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Why does it work?

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By: Tim Lehman

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Each median splits the triangle into two equal pieces. By definition, each median connects a vertex to the midpoint on the opposite side. In the example above, D is the midpoint of segment AC. Thus, AD=DC. Triangles ADB and DCB therefore have the same base and the same height. We then know they have the same area. Using the same argument, the three medians will divide the triangle into six triangles of equal area. By combining any two of them, we will have a shape with 1/3 the original area.