No, it is not necessarily true.
line
two-fold
A line has two fold rotational symetry.
It has rotational symmetry of order 2.
True. When you fold the paper so that point P lies on the fold line and the two sides of line L match up, the crease formed will be parallel to line L. This is because the fold bisects the angle formed by the two sides of line L, creating two congruent angles, which in turn makes the crease line parallel to line L.
A parallelogram has rotational symmetry of order 2.
Are you referring to the Marquise Cut in Diamond jewelry? This is in the shape of a pointed oval; it would two-fold rotational symmetry.
Yes, it does.
Yes, it does.
it has two folds.
Yes. An ellipse (oval) has two lines of symmetry, but not a rotational symmetry. A parabola has one line and no rotation.
Symetrical line