No, they are not.
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Yes, it is possible for a shape to have at least one pair of parallel lines and no lines of symmetry. For example, an irregular trapezoid has one pair of parallel sides but lacks any lines of symmetry due to its uneven angles and side lengths. This demonstrates that parallel lines and symmetry are independent properties in geometric shapes.
a trapezoid has a pair of symmetry lines but a square diamond or parallelogram all sides are parallel
There are no lines of symmetry; However, the lines opposite are parallel to each other
A general trapezoid is a 4 sided quadrilateral with a pair opposite parallel lines of different lengths and no lines of symmetry But an isosceles trapezoid has the same properties as above except that it has 1 line of symmetry
The shape has to be a parallelogram since it has no lines of symmetry and all sides are equal and parallel