Median(s) of a Triangle
Definition

A median of a triangle is a segment from a vertex of the triangle, to the midpoint of the side opposite that vertex of the triangle.

Since all triangles have three vertices and three opposite sides, all triangles have three medians.

Median of a Triangle Example

Demonstration
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The three medians of any triangle intersect at a common location called the centroid.


The centroid of any triangle, whether it is an acute triangle, a right triangle, or an obtuse triangle, occurs inside the triangle.


To visually verify this statement, please select "SHOW ALL MEDIANS" in the demonstration applet above, then drag the vertices to create acute, right and obtuse triangles.