Centroid(G) - the intersection of three medians of triangle. Also, it means the center of gravity of the triangle.

Median- A straight line passing from a point of a triangle to the midpoint of the opposite side.

Observation

We can see the result that for any triangle the three medians of a triangle are concurrent and that the point of concurrence, the centroid, is two-thirds the distance from each vertex to the opposite side.

Let me prove this fact.

Here is another proof

Suggestion

I think that students can understand centroid by consrtructing the three medians.

GSP is the appropriate tool which makes sense the concurrence of centroid and the property that the point of concurrence is two-thirds the distance from each vertex to the opposite side.