Not all 4 sided quadrilaterals have lines of symmetry although some of them do have lines of symmetry.
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All kites are quadrilaterals, but quadrilaterals are not kites.
All parallelograms are quadrilaterals but all quadrilaterals are not necessarily parallelograms
All quadrilaterals have 4 sides
All 4 sided parallelograms are quadrilaterals.
Not all 4 sided quadrilaterals have lines of symmetry.