No, shapes with odd numbers of sides do not always lack parallel sides. For example, a trapezoid is a four-sided shape (even number of sides) that has one pair of parallel sides, while an irregular pentagon (five sides) can have no parallel sides at all. The presence of parallel sides depends on the specific properties and measurements of the shape, not solely on whether the number of sides is odd or even.
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Infinitely many. Every regular polygon with 2n sides has n pairs of parallel sides. Then there are irregular polygons which can have parallel sides. And there are also irregular shapes which have parallel sides.
Circles
Well If you are looking for a four sided shape with no parallel sides it is called a trapezium.
No, a parallelogram cannot be a hexagon. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length, while a hexagon is a polygon with six sides. These are two different shapes with different numbers of sides.
Angle