A rectangle in which all sides are equal is a SQUARE

It has all the properties of a rectangle viz
Opposite sides are equal
Opposite angles are equal
Diagonals bisect each other
Diagonals are equal.

Additional Property:  
Digonals bisect at right angles. 

def

properties

angles

additional

So, SQUARE is a special quadrilateral.
It is a regualr quadrilateral.

regualr

A = (-4.973283203521161, 0.03282711082147849)
B = (2.8447792447434743, 0.06460785248109088)
poly1, f, g, h, i, C, D = Polygon(A, B, 4)
distanceAB = Distance(A, B)
TextAB: Name[A] + (Name[B]) + " = " + distanceAB
distanceBC = Distance(B, C)
TextBC: Name[B] + (Name[C]) + " = " + distanceBC
distanceCD = Distance(C, D)
TextCD: Name[C] + (Name[D]) + " = " + distanceCD
distanceDA = Distance(D, A)
TextDA: Name[D] + (Name[A]) + " = " + distanceDA
j = Segment(A, C)
k = Segment(B, D)
E = Intersect(k, j)
α = Angle(C, E, D)
β = Angle(D, E, A)
γ = Angle(A, E, B)
δ = Angle(B, E, C)
a = true
b = true
c = true
d = true
e = true