Chapter 6  

Triangle and its properties

Median of a triangle

Median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.

A median connects a vertex of a triangle to the mid-point of the opposite side.
In the ∆ ABC, the line segment AD joining the mid-point of BC to its opposite vertex A is called a median of the triangle.

Properties of Median of a Triangle

Every triangle has exactly three medians one from each vertex and they all intersect each other at the triangle's centroid.

  • The 3 medians always meet at a single point, no matter what the shape of the triangle is.
  • The point where the 3 medians meet is called the centroid of the triangle. Point O is the centroid of the triangle ABC.
  • Each median of a triangle divides the triangle into two smaller triangles which have equal area.
  • In fact, the 3 medians divide the triangle into 6 smaller triangles of equal area. 

In ∆ ABC, three medians are AD, CE and BF and they are intersecting the point O which is centroid of the triangle.