Two lines that coincide look and act exactly like a single line.
If you have one straight line, there are an infinite number of planes in which it lies.
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Parallel Lines - Skew lines are lines that do not intersect and do not lie in the same plane. If two lines lie in the same plane they they must either intersect or they are parallel.
If lines lie in two planes, then the lines are coplanar.
Parallel Lines.
In a Euclidean plane (the one which we are all familiar with), they would be parallel lines.
Perpendicular lines.