3quilaterals Applet

This applet explores the geometric theorem that for any three equilateral triangles which share a common vertex, the midpoints of the lines joining non-shared vertices of pairs of adjacent triangles themselves always form an equilateral triangle. The applet allows the user to quickly see that the claimed relationships are preserved, and maybe gain some intuition as to why the theorem is true before going through the proof.
[If your browser refuses to run this app in an iFrame then you might try to run it in a new "insecure" window]