## Objective:

To illustrate that the medians of a triangle concur at a point (called the centroid), which always lies inside the triangle.

### Theory:

A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid-point on the opposite side of the triangle.

The centroid is also called the center of gravity of the triangle. If you have a triangle plate, try to balance the plate on your finger. Once you have found the point where it will balance, that is the centroid of that triangle.

### Properties of the centroid:

- It is always located inside the triangle.
- The centroid divides each median in a ratio of 2:1. In other words, the centroid will always be 2/3 of the way along any given median.
- In below images, c is centroid for △ABC.

Fig.(a) Acute-angled Fig.(b) Right-angled Fig.(c) Obtuse-angled