Where is the centroid of a triangle located?

The centroid of a triangle is defined as the point where the three medians intersect. A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. The centroid has several important properties; one of them is that it is the center of mass of the triangle, balancing it perfectly if made of uniform material.

A key characteristic of the centroid is that it is always located inside the triangle, regardless of the type of triangle—whether it is acute, right, or obtuse. This foundational property of centroids ensures that they provide reliable and consistent references within triangle geometry. Thus, identifying the centroid as always being inside the triangle is fundamental to understanding triangle properties and spatial relationships in geometry.