no? because in order to be a quadrilateral you need 4 sides. a pair of parallel lines in just 2 lines. parallel lines also never touch.
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A quadrilateral that has only one pair of parallel sides (the other pair not parallel) is a trapezium.
Yes, a trapezoid is a quadrilateral with only one pair of parallel sides.
Only if it is a trapezoid (US usage) with one set of parallel sides, or a parallelogram with both sets of opposite sides parallel. The term quadrilateral only means that the shape has 4 sides.
I would be seriously concerned if a quadrilateral had more than two pairs of opposite sides parallel! A quadrilateral with two pairs of opposite sides parallel is a parallelogram.
There are actually I think two with only two parallel sides. A square and a rectangle