median

The median of a triangle is a line segment joining a vertex with the midpoint of the opposite side.

In the next figure, $A{A}^{\prime }$ is a median. That is, $B{A}^{\prime }=A^{\prime }C$, or equivalently, $A^{\prime }$ is the midpoint of $BC$.

If the length of the three sides of the triangle are known, the length of the medians can be found by means of Apollonius theorem.

Title	median
Canonical name	Median
Date of creation	2013-03-22 11:44:01
Last modified on	2013-03-22 11:44:01
Owner	CWoo (3771)
Last modified by	CWoo (3771)
Numerical id	18
Author	CWoo (3771)
Entry type	Definition
Classification	msc 51-00
Classification	msc 55-00
Classification	msc 55-01
Related topic	Triangle
Related topic	ApolloniusTheorem
Related topic	Orthocenter
Related topic	CevasTheorem
Related topic	Centroid
Related topic	ProofOfApolloniusTheorem2
Related topic	ParallelogramLaw
Related topic	TrigonometricVersionOfCevasTheorem
Related topic	ProofOfParallelogramLaw
Related topic	HeightOfATriangle
Related topic	Cevian