What is the center of gravity of a triangle? What are its properties?

What is the center of gravity of a triangle? What are its properties?

The center of gravity is the intersection of the three sides of a triangle
Some properties of the center of gravity: the ratio of the distance from the center of gravity to the vertex and the distance from the center of gravity to the midpoint of the opposite side is 2:1; the area of the three triangles composed of the center of gravity and the three vertices of the triangle is equal; the sum of the squares of the distances from the center of gravity to the three vertices of the triangle is the smallest

The properties of triangle center of gravity
It's said in the book that a rope is tied to the center of gravity of the triangle. If the hand holds the rope, the triangle will be balanced. Why
Is the center of gravity of a physical triangle the same as that of a mathematical triangle?

The center of gravity can be seen as follows: all the masses are concentrated on this point. It can be considered that only at this point can there be mass, and there is no mass in other places. To tie a rope on the center of gravity and hold the rope can be regarded as exerting a force directly above the particle. At this time, the particle is subjected to two forces: gravity and rope application