A square or a rhombus
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rhombus. The rhombus is a quadrilateral with all sides equal in length. It is also a parallelogram, so opposite sides are parallel and equal in length, and opposite angles are equal.
Yes. A parallelogram is defined as having opposite sides that are parallel and equal in length, and opposite angles that are equal.
That's an "isosceles" triangle. By the way ... it's enough to say that two sides are equal. That automatically guarantees that the angles opposite them are equal.
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.
Rhombus