square
A parallelogram is a four sided shape where opposite sides are parallel and equal lengths. If you mean that ALL sides are equal lengths, you are looking for a rhombus.
A rhombus is a shape having two acute angles and four equal sides.
A rectangle has four sides with two equal lengths.
Rectangle
A "parallelogram" technically is a shape where opposite sides are equal and any shape with four sides is a "quadrilateral". Every square has four sides of equal length, so a square is both a parallelogram and a quadrilateral. A rhombus(or diamond shape) can have four sides of equal length and can be a parallelogram as well, so either are possibilities.
The rectangle
A square is a two-dimensional shape with four equal sides and four right angles.
No shape has four equal sides and four different angles - either there are two pairs of equal angles, or all four angles are the same; or all sides are not the same length.
There is no such shape. If the four sides are equal it MUST be a parallelogram.
You are a square
A geometric shape with four sides, where all four sides are of an equal length.