A square has rotational symmetry to the order of 4
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Rotational symmetry refers to symmetry of the figure when it is rotated about a single point in the same plane. Lines of symmetry apply to reflections. You do not have lines of rotational symmetry.
A circle, square, and a triangle all have rotational symmetry.
No. A square is a plane figure and conventionally for plane figures symmetry is considered in terms of rotation about a point or an axis (in the plane of the figure) but not a plane outside the plane of the square.
Yes it does. As long as it has a symmetry without rotation. If you do the rotation either way it does have symmetry. :)
Yes, 180 degrees. In the degenerate case that the parallelogram is a square, then 90 degrees.