No, it does not. Take a sheet of A4 paper and fold it across the diagonal, and you will see that the two halfs do not line up.
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A rectangle.
It has a line of rotational symmetry - along the diagonal.
yes
If you draw a diagonal line from corner to corner of a parallelogram, that is a line of symmetry.
No, a non-square rectangle has two: the horizontal and the vertical. A square has four lines of symmetry: the horizontal, the vertical, and two diagonal lines.