Median of a triangle definition - Math Open Reference

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Medians of a Triangle

From Latin: medianus - "of the middle"

A median of a triangle is a line joining a vertex to the midpoint of the opposite side.
A triangle therefor has three medians.

Try this Drag the orange dots on each vertex to reshape the triangle. Notice the three medians all meet at one point.

(If there is no image below, see support page.)

A median of a triangle is a line from a vertex of the triangle to the midpoint of the side opposite that vertex. Because there are three vertices, there are of course three possible medians. One of the fascinating things about them is that no matter what shape the triangle, all three always intersect at a single point. This point is called the centroid of the triangle.

Properties

There are some fascinating properties of the medians of a triangle:

The fact that the three medians always meet at a single point is interesting in its own right
Each median divides the triangle into two smaller triangles which have the same area
The centroid (point where they meet) is the center of gravity of the triangle

Adjust the triangle above by dragging any vertex. Convince yourself that the three medians (green lines) always intersect at a single point. You can also visually estimate that the area facts given above are true.

Try this

Make any triangle about 12 - 24" wide from cardboard. Make it as lop-sided and irregular as you can.
Draw a median on the cardboard triangle. Any one will do.
At the point where the median meets the side of the triangle make a small hole near the edge. Tie a string through it.
When you hold up the triangle by the string, the median line should be vertical - exactly in line with the string.(see figure below)
Why?

Related triangle topics

General

Triangle types

Triangle centers

Congruence and Similarity

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