So AB=BC=DC=AD

Angle A= Angle B= Angle C= Angle D=90 degrees.

Because AB=AA'+A'B

BC=BB'+B'C

DC = cc+cc

AD=DD'+AD '

AA'=BB'=CC'=DD '

So AD = A' B = B' c = DC.

So right triangle AA'D is equal to triangle A'BB', triangle B'CC' and triangle DD'C (SAS).

So A'D'=A'B'=B'C'=C'D'

Angle 2= Angle 3

So the quadrilateral A'B'C'D is a diamond.

Because angle A+ angle 1+ angle 2= 180 degrees.

So angle 1+ angle 3=90 degrees.

Because angle 1+ angle 3+ angle B'A'D'= 180 degrees.

So the angle B'A'D'=90 degrees.

So quadrilateral A'B'C'D is a square.