Answer:
To show that all three medians of a triangle intersect at the same point, we can use the property that the midpoint of each median is the centroid of the triangle.
The centroid of a triangle is a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. This means that the centroid divides each median in a 2:1 ratio, with two thirds of the median length being on one side of the centroid and one third on the other side.
Since the centroid is the same for all three medians, it follows that all three medians must intersect at the same point, which is known as the centroid or the center of gravity of the triangle. This point is denoted by the letter G.
Therefore, we can conclude that all three medians of triangle ABC intersect at point G, which is the centroid of the triangle.