A centroid of a triangle is the point where the three medians of the triangle meet.

The point where the medians of a triangle meet is called the centroid of the triangle. The centroid is often referred to as the "center of mass" or the "center of gravity" of the triangle. It is denoted by the letter G.


Medians are line segments that connect each vertex of a triangle to the midpoint of the opposite side. Every triangle has three medians, and they intersect at a single point, which is the centroid.


1. The centroid divides each median in a 2:1 ratio, where the longer segment is closer to the vertex.
2. The centroid is located two-thirds of the distance from each vertex to the midpoint of the opposite side.
3. The centroid is always inside the triangle, never on the triangle itself or outside of it.
4. The centroid is the balancing point of the triangle. If the triangle were cut out of cardboard, the centroid would be the point where it could be balanced on the tip of a pencil.


The centroid of a triangle has several important properties and applications:
1. The centroid is the center of mass of a triangle. In physics and engineering, it is used to determine the stability and equilibrium of objects.
2. The centroid is used in the construction of the centroidal axis, which helps in calculating the moment of inertia of a triangle.
3. The centroid is an important point in geometric proofs and constructions.
4. The centroid divides the triangle into six smaller triangles with equal area.
5. The centroid is used in various mathematical problems, such as finding the equation of a line passing through the centroid and another point.

In conclusion, the point where the medians of a triangle meet is called the centroid of the triangle. It is a significant point with various properties and applications in mathematics and physics.