Yes. Parallel means they they are always the same distance and they never intersect, and this could only mean on the same plane. However, the proof that it works is a little harder than one might think.
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Two lines that do not intersect on the same plane are Parallel lines.
Parallel lines.
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.
They are parallel lines
Parallel