Median (of a triangle)

A straight line (or its segment contained in the triangle) which joins a vertex of the triangle with the midpoint of the opposite side. The three medians of a triangle intersect at one point, called the centre of gravity, the centroid or the barycentre of the triangle. This point divides each median into two parts with ratio $2:1$ if the first segment is the one that starts at the vertex. The centroid lies on the Euler line.

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J. Hjelmslev has shown that also in hyperbolic geometry (cf. Lobachevskii geometry) the meridians of a triangle intersect at a point.

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