A median in a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. Each triangle has three medians, one from each vertex, and they all meet at a point called the centroid.
The centroid is an important point in a triangle because it is the balance point or center of mass of the triangle. The medians divide each other in a 2:1 ratio, meaning that the segment connecting the vertex to the centroid is twice as long as the segment connecting the centroid to the midpoint of the opposite side. This property makes the medians essential in various geometric calculations and constructions.