No, parallel lines cannot ever intersect. The have identical slopes. Therefore, they will always remain parallel.
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are two lines that are not parallel, coplanar, and do not intersect
Parallel lines never intersect
If the two lines lie in the same plane, and they do not intersect, then they are parallel. If they are not in the same plane, and do not intersect, then they are called skew lines.
Coplanar lines that do not intersect are called parallel lines.
2 parallel lines are lines that will never intersect