An irregular parallelogram rotates 360° about the midpoint of its diagonal. how many times does the image of the parallelogram coincide with its preimage during the rotation?

How do you do this geometry problem

The number of revolutions of two pulleys is inversely proportional to their diameters. if a 24-inch diameter pulley making 400 revolutions per minute is belted to an 8-inch diameter pulley, find the number of revolutions per minute of the smaller pulley.

1. are the triangles similar and if so why? what is the value of x? show your work.