Properties of Median

The median is a segment that starts at one of the 3 vertices of the triangle and ends at the midpoint of the opposing base.

In the below figure the three medians are Ma=AP, Mb=BQ and Mc=CR.

The medians of a triangle always intersect in one point (the centroid).

Properties of Median

1. The medians of a triangle always intersect in one point (the centroid).

2. The centroid always lies inside the triangle.

3. The centroid cuts every median in the ratio 2:1, i.e. the distance between a vertex and the centroid is twice as long as the distance between the centroid and the midpoint of the opposite side.

4. The lengths of the medians are defined by the following equations

5. The area of a triangle can be expressed in terms of the medians by