All four sides of a rhombus are equal length.
If a parallelogram has all four sides the same length it's called a square.
I am a rhombus. I don't need to prove that my opposite sides are parallel. If I'm a quadrilateral with four sides that are the same length, then I am definitely a rhombus.
This is called a Parallelogram. Each pair of opposite sides will then be the same length. If all four sides are the same length, and opposite sides are parallel, then it is a rhombus. NB: If all four sides are the same length then the opposite sides must be parallel.
A square if all sides are the same length, otherwise a rectangle.
A four-sided shape with only 2 sides the same length is called a rhombus.
A shape with opposite sides parallel and of the same length and four right angles is a rectangle.