Median (geometry)

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The triangle medians and the centroid.
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The triangle medians and the centroid.

In geometry, a median of a triangle is a line joining a vertex to the midpoint of the opposite side. It divides the triangle into two parts of equal area. The three medians intersect in the triangle's centroid or center of mass, and two-thirds of the length of each median is between the vertex and the centroid, while one-third is between the centroid and the midpoint of the opposite side.

Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid.

[edit] The length of the median

Applying Stewart's theorem one gets:

m = \sqrt {\frac{2 b^2 + 2 c^2 - a^2}{4} }

where a is the side of the triangle whose midpoint is the extreme point of median m.

[edit] External links

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