Nested Median Triangles[br]The three dotted line segments, MA, NE, ID are called medians of the triangle.[br]They go from a vertex to the midpoint of the opposite side, and all pass through point P, the centroid.[br]If the midpoints of the triangle, E, D, A form a new triangle, and the medians of this triangle are drawn, [br]they look as though they pass through the same point P.[br]Experiment with the slider to add more triangles formed by the midpoints of the triangles.

1- Can you prove that the original three medians intersect at the same point?[br]2- Can you prove that the newly created medians also intersect at the same point?[br]2- Can you prove that the six small triangles formed by the original medians have equal areas?