Given a quadrilateral, prove it is a square. Consider this game.


  You have a perfect ruler and a perfect protractor. You are also able
  to observe perfectly if two lines are parallel.
  
  Is it possible to prove that a given quadrilateral is a square, using
  exactly 3 steps?


For example, a proof using 4 steps would be this.


  
  Observe that opposite sides are parallel (two steps).
  The angle between the diagonals is 90 degrees. 
  The angle between any two adjacent sides is 90 degrees.
  


My gut feeling is that it is not possible to do this in 3 steps and that the minimum would be 4. But how would one prove this?
I don't believe this is possible.

A quadrilateral has 4 degrees of freedom, to similarity: place the polygon so it has two of its vertices at $(0,0)$ and $(1,0)$.  Then the other two points are free to be (almost) anywhere.  In order to find one of these points we must make two measurements, and the other is completely independent, so there is no measurement that can be used to constrain both.
Three steps :

1- the diagonals meet at their midpoint (or is it two steps one for each diagonal) : this ensures we have a parallelogram

2- the diagonals are of equal length

3- the diagonal meet at $90$ degrees.