Interactive asymmetric propeller

Author:
alfinio
The dotted segments connect vertices of different triangles. The midpoints of the dotted segments are connected (click at the button).
The red triangle seems to be equilateral. Provide empirical evidence or a convincing argument to support this conjecture. You can modify the problem. For instance, what if the equilateral triangles are not congruent? In what other ways can you modify the problem?