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Yes
yes, or else the lines would no longer be parallel
A quardrilateral with 1 pair of parallel lines and have no equal sides is a trapezium.
Yes, they do. By definition, lines that never intersect must be parallel, so all non-parallel lines must intersect at some point. Given that they are normal lines (y=mx+b) they will always have a point that suffices the equation when they are set equal to each other.
Parallel lines