Definition
of the Centroid of a Triangle
The Centroid is a point of concurrency of the triangle. It is the point where all 3 medians intersect and is often described as the triangle's center of gravity or as the barycent.
Properties of the Centroid- It is formed by the intersection of the medians.
- It is one of the points of concurrency of a triangle.
- It is always located inside the triangle (like the incenter, another one of the triangle's concurrent points)
- 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. See bottom set of pictures.
Picture of Centroid of an Acute Triangle
![Picture of Centoid of a Triangle](../images/triangle-concurrency-points/picture-of-centroid-of-a-triangle.png)
Picture of Centroid of an Obtuse Triangle
![Centroid of Obtuse Triangle](../images/triangle-concurrency-points/centroid-picture-obtuse-triangle_medium.png)
Pictures of the 2:1 ratios formed by centroid and medians
![Picture of Centroid Ratios](../images/triangle-concurrency-points/centroid-ratios_1.png)
![Picture of Centroid Ratios 2](../images/triangle-concurrency-points/centroid-ratios_2.png)
![Picture of Centroid Ratios 3](../images/triangle-concurrency-points/centroid-ratios_3.png)
Practice Problems
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Related Links:
- Triangles
- Triangle Types
- Interactive Triangle
- images
- Free Triangle Worksheets