Nested Median Triangles
The three dotted line segments, MA, NE, ID are called medians of the triangle.
They go from a vertex to the midpoint of the opposite side, and all pass through point P, the centroid.
If the midpoints of the triangle, E, D, A form a new triangle, and the medians of this triangle are drawn,
they look as though they pass through the same point P.
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?
2- Can you prove that the newly created medians also intersect at the same point?
2- Can you prove that the six small triangles formed by the original medians have equal areas?