Yes, that's true.
I think you'd also find that one right angle is enough to do it.
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Not necessarily. A parallelogram is a quadrilateral with 2 sets of 2 parallel sides. Only rectangles and squares have right angles as all four angles - a rectangle is a "special" parallelogram that has all four angles equal; a square is a "special" rectangle that has all four sides of equal length.
Rectangle and square
A rectangle has four angles of 90° each, also known as right angles. The special case is the square, which is a rectangle with four equal sides.
it could be a square or a rectangle. its a square if all four sides are congruent, but if not, its a rectangle.
a rectangle has four right angles and opposite sides are all the same length This means that a parallelogram is not always a rectangle, but a rectangle is always a parallelogram, by definition.