Geometric Art: Problem 1202: Four Squares. Graphic Design, iPad Apps

The figure below shows four squares AA₁BA₂, BB₁CB₂, CC₁DC₂, and DD₁AD₂. Prove that the quadrilaterals A₁B₂C₁D₂ and B₁A₂D₁C₂ are congruent parallelograms.
  

See also:
Original problem 1202