If both the pairs of opposite sides are parallel,
 then it is a Parallelogram

If all the 4 sides of ABCD are same,
then it becomes a rhombus.

Rhombus

A = (-2.780412029007908, 0.22351156077915288)
B = (3.2360515501501714, -1.026733237131537)
f = Segment(A, B)
D = (0.07985472035720176, 5.658018384572873)
g = Line(D, f)
h = Segment(A, D)
i = Line(B, h)
C = Intersect(g, i)
j = Segment(D, C)
k = Segment(B, C)
α = Angle(A, D, C)
β = Angle(C, B, A)
γ = Angle(B, A, D)
δ = Angle(D, C, B)
text2: "∠A =" + γ + ",∠C =" + δ + ", ∠B=" + α + ",∠D=" + β + "
Opposite angles ∠A =∠C &∠B=∠D"
text1: "AB =" + f + ",DC =" + j + ",AD =" + h + ",BC=" + k + "
∴Opposite sdes AB =DC,AD = BC"
sumofangles: α + γ
text3: "Sum of adjacent angles = 
∠A+∠B=" + γ + "+" + α + "=" + sumofangles + ""
l = Segment(A, C)
m = Segment(D, B)
E = Intersect(l, m)
distanceDE = Distance(D, E)
TextDE: Name[D] + (Name[E]) + " = " + distanceDE
distanceEB = Distance(E, B)
TextEB: Name[E] + (Name[B]) + " = " + distanceEB
distanceAE = Distance(A, E)
TextAE: Name[A] + (Name[E]) + " = " + distanceAE
distanceEC = Distance(E, C)
TextEC: Name[E] + (Name[C]) + " = " + distanceEC
text4: "Lengths of DE = BE =" + distanceDE + " &
Lengths of AE = EC = " + distanceAE + "
So diagonals AC & BD bisect each other."
a = true