Quadrilateral Tessellation

This is a tiling of quadrilaterals. But what motions take the pink quadrilateral onto an adjacent tile?

When it looks like a square (a regular quadrilateral), it is difficult to tell. Use the blue dots to change the pink tile for clues as to the actual motions used.

What properties does the tile always have that allows it to be moved in this way?

Posted at mathhombre.blogspot.com.

John Golden, Created with GeoGebra