Centroid (G)

The centroid of a triangle is the intersection of the three medians, and it lies at 2/3 of the way from any vertex to the midpoint of the opposite side.

Keywords: centroid, medians, center of gravity, balance point

Prerequisites: triangle · Difficulty: beginner

Imagine you have a triangle made of a piece of cardboard. The centroid is the triangle's "center of gravity" or "balancing point." If you could put your finger right on the centroid, the triangle would balance perfectly!

How do we find it?

We find the centroid by drawing lines called medians.

A median is a line that connects a corner (vertex) of the triangle to the middle (midpoint) of the opposite side.

Every triangle has three medians, and they all cross each other at a single point. That point is the centroid!

Fun Facts

• The centroid is always inside the triangle, no matter how you shape it.
• The centroid divides each median into two parts. One part is twice as long as the other. The part connected to the vertex is the longer one.