The diagonal of ABCD paralleogram is BD=2. The angles of triangle BCD are all equal. What is the perimeter of parallelogram?

Since all the angles of triangle BCD are equal, that means
that the triangle BCD is equilateral, therefore BD = BC = CD =
2.

Since ABCD is parallelogram, then BC=AD = 2 and AB = CD
= 2.

The perimeter of the parallelogram ABCD
is:

P = AB+BC+CD+AD

P =
4*AB

P = 4*2

P = 8
units

The requested perimeter of the
parallelogram ABCD is of 8 units.