It means 4 lines of symmetry as for example a square has 4 lines of symmetry
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This is a little bit like asking why a square has four sides. A regular pentagon is defined in such a way as to require that it has 5-fold rotational symmetry.
It has rotational symmetry of order 2.
Yes, it does.
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Parallelograms: 2-fold Square: 4-fold n-fold symmetries refer to rotational symmetries. Consequently, any symmetries about axes that these and other quadrilaterals may have are not relevant to this question.