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.