Proof of the concurrency of the medians of a triangle


P and Q are the midpoints of AC and BC respectively.

PQ is parallel to and one half the length of AB since it joins the mid-points of AC and BC.

Hence triangle PGQ is similar to triangle BGA and we have:

Median BP cuts AQ at the trisection point of AQ closest to Q and similarly median CR cuts AQ at this same point.


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