Porisma
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Vectors: magnitude, direction and products

Prove the centroid lies on all three medians · Diagrams

Centroid and all three medians

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Triangle OAB has midpoints M of OB, N of OA and R of AB. All three medians meet at G. A second panel relabels O as C. Matching side ticks identify the midpoints and labels show AG:GM=2:1. The triangle is nondegenerate; the diagram imposes no coordinates.
Triangle OAB has midpoints M of OB, N of OA and R of AB. All three medians meet at G. A second panel relabels O as C. Matching side ticks identify the midpoints and labels show AG:GM=2:1. The triangle is nondegenerate; the diagram imposes no coordinates.
Triangle OAB has midpoints M of OB, N of OA and R of AB. All three medians meet at G. A second panel relabels O as C. Matching side ticks identify the midpoints and labels show AG:GM=2:1. The triangle is nondegenerate; the diagram imposes no coordinates.
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