Why do these equations hold? Let's prove the three medians of a triangle are concurrent and the centroid is (2/3) the distance from a vertex to the midpoint of the opposite side.
Let's begin by proving the concurrency of the medians. In order to prove concurrency of the medians, let's start by constructing D to be the midpoint of the segment AC and E to be the midpoint of the segment AB. Then, construct the segments BD and CE. Let their intersection point be labeled G. Then construct the segment DE.,