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median (Definition)

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

In the next figure, $ AA'$ is a median. That is, $ BA'=A'C$, or equivalently, $ A'$ is the midpoint of $ BC$.

\includegraphics[scale=0.5]{median}

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.



"median" is owned by CWoo. [ full author list (3) | owner history (2) ]
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See Also: triangle, Apollonius theorem, orthocenter, Ceva's theorem, centroid, proof of Apollonius theorem, parallelogram law, trigonometric version of Ceva's theorem, proof of parallelogram law, height, cevian

Keywords:  Triangle, Geometry
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Cross-references: Apollonius theorem, sides, length, opposite side, midpoint, vertex, line segment, triangle
There are 14 references to this entry.

This is version 10 of median, born on 2001-10-06, modified 2007-10-08.
Object id is 142, canonical name is Median.
Accessed 9168 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
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