A parallelogram always has one set of parallel lines, plus another set also.
A trapezoid (trapezium) always has exactly one set of parallel lines and no more.
Any shape with more than four sides can have one set of parallel lines, but doesn't
necessarily have to.
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I don't think this is possible. there is not a quadrilateral with these qualities. If it is a quadrilateral, it will automatically have parallel lines, but there is not one that has both. The closest one would be the trapezoid, with a set of parallel lines, but no right angle. The square and rectangle have two sets of parallel lines and 4 right angles.
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Trapezium
A trapezoid, trapezium and a pentagon have only 1 set of parallel linesRead more: What_3_shapes_have_1_set_of_parallel_lines
trapezoids