Amedian of a triangle is a segment joining a vertex to the midpoint of the opposite
Chapter 8, Problem 42(choose chapter or problem)
Amedian of a triangle is a segment joining a vertex to the midpoint of the opposite side. Show that the centroid of a triangle lies on each of its medians, at a distance two-thirds down from the vertex. Then use this fact to prove that the three medians intersect at a single point. Hint: Simplify the calculation by assuming that one vertex lies at the origin and another on the x-axis.
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