# Median (of a triangle)

From Encyclopedia of Mathematics

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.

#### Comments

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

#### References

[a1] | H.S.M. Coxeter, "Introduction to geometry" , Wiley (1989) |

**How to Cite This Entry:**

Median (of a triangle).

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Median_(of_a_triangle)&oldid=37563

This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article