An infinite number of shapes.
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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 concave is not a shape. It is a characteristic of one. It is like asking how many parallel lines a small has.
At least 4 lines, but no matter how many lines, every line has to be parallel with at least one other line.
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2 parallel lines * * * * * The above answer is not wholly correct. A hexagon can have one, two or three pairs of parallel lines: a regular hexagon has 3 pairs.