What other angles could they be? The hypotenuses are all the same length, we don’t need to prove that as it’s part of the design of the initial setup. The triangles are all the same, that’s likewise by design. They are all transformed on the plane in the same way.
The only possible shape they can make is a square when all that is taken into account.
The only possible shape they can make is a square when all that is taken into account.