Median of a triangle
A median of a triangle is a cevian of the triangle that joins one vertex to the midpoint of the opposite side.
In the following figure, 
is a median of triangle 
.
![[asy] import markers; pair A, B, C, M; A = (1, 2); B = (0, 0); C = (3, 0); M = (midpoint(B--C)); draw(A--B--C--cycle); draw(A--M); draw(B--M, StickIntervalMarker(1)); draw(C--M, StickIntervalMarker(1)); label("$A$", A, N); label("$B$", B, W); label("$C$", C, E); label("$M$", M, S); [/asy]](http://latex.artofproblemsolving.com/a/e/5/ae531958c09b155c0dca21e9cd9b9bb01d391fb9.png)
Each triangle has 
medians. The medians are concurrent at the centroid. The centroid divides the medians (segments) in a 
ratio.
Stewart's Theorem applied to the case 
, gives the length of the median to side 
equal to
This formula is particularly useful when 
is right, as by the Pythagorean Theorem we find that 
.
See Also
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