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Yes - a square is a special case of a parallelogram in which all sides are equal length and all angles are 90o. Every square is a rectangle, a rhombus, a parallelogram, and a regular quadrilateral.
No.
A parallelogram can be a square, but never can a square be a parallelogram. A square is defined as having all four sides the same and all four right angles. A parallelogram has to have two pairs of parallel sides.
No, as the angles of a square are all equal, whereas the angles of a parallelogram typically aren't. There are other examples, as well; this is just one difference.
1. All 4 sides same length 2. Is a parallelogram 3. Opposite angles are equal 4. Can be a square if all angles are 90°