In what ratio does the centroid of Δ divide each median.

Explanation -

The centroid of a triangle divides each median into two segments in the ratio of 2:1. This is known as the Centroid Theorem.

If G is the centroid of a triangle, and A, B, and C are the vertices of the triangle, then AG is 2/3 of the length of the median from vertex A, BG is 2/3 of the length of the median from vertex B, and CG is 2/3 of the length of the median from vertex C.

Mathematically, if D is the midpoint of side BC, E is the midpoint of side CA, and F is the midpoint of side AB, then:

 GD = 2/3 AD , GE = 2/3 BE and  GF = 2/3 CF

This property holds true for any triangle.

So the centroid of a triangle divides each median into two segments in the ratio of 2:1.