Each pair of opposite sides has equal slopes.
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parallelograms, and rectangles (parallelograms)
No shape is a square but not a parallelogram as all squares are parallelograms: All parallelograms have opposite sides parallel and of equal length, and opposite angles are equal. All squares have opposite sides that are parallel and of equal length, and opposite angles are equal; thus all squares are parallelograms. However, all squares also have all angles equal to 90o and all four sides equal, but some parallelograms have angles not all 90o and/or not all four sides of equal length; thus not all parallelograms are squares.
I'm not sure what you're asking for, but parallelograms always have parallel sides which are equal in length.
No but they are 4 sided quadrilaterals.
Parallelograms (if the equal sides are opposite one another) or kites (if they are adjacent).