Try a square or parralellogram.
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
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.
A Paralellogram
A quadrilateral
a rhombus
The opposite sides in a parallelogram are parallel and the same length. However, they are not angles at 90 degrees (right angles).
A square fits into the description.
A Rhombus
Yes. By definition, opposite sides are equal (i.e. same length) and parallel.
A TRAPEZIUM. Trapezia can be SYMMETRIC or ASSYMETRIC. That is Non-parallel sides can be of the same length or of different lengths/ intersext at different angles to the parallel lines.
A shape with opposite sides parallel and of the same length and four right angles is a rectangle.