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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 of course!
Its a diamond :]
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.