Centroid of a triangle

## 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 triangles(a, b & c).

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

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