Napolean's Theorem
In this applet, we have the following:
A modifiable white triangle (with red vertices)
Equilateral triangles built off each side of this white triangle.
The centroid of each of these equilateral triangles (points G, H, & I).
Triangle GHI.
Drag each of the red vertices of the white triangle around.
1) What seems to be true?
2) Use the tools of GeoGebra to informally show that your assertion in (1) is correct!
3) Keep dragging the red vertices of the white triangle around. Does your assertion still hold true?