In Euclidean geometry they cannot.
In other geometries they can meet at various points, depending on the configuration of the space.
In projective geometry, for example, they meet at the "point at infinity".
In physics, though, parallel rays (of light, for example), can be made to meet at the focus of a lens or mirror.
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As long as they are not parallel, they will meet at an "edge", which is just a straight line.
Lines that meet are not parallel, and parallel lines never meet.
Because of the way parallel lines are defined. Parallel lines never meet, but to qualify as parallel lines, additional conditions may apply. From Wikipedia: "Two lines in a plane that do not intersect or meet are called parallel lines." Emphasis added.
Being 'Parallel' , they only meet at INFINITY.
No, in Euclidean geometry they do not meet.