No point in common.
That is correct.
More common explanation is that even if you extend the lines in either direction, they would not touch (i.e. have a common point.)
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no parallel lines
parallel lines are diagonal lines or increasing lines
Skew lines are not parallel. Parallel lines are across from each other in some way and are exactly parallel.
It can, but it need not have parallel lines.
There are no parallel lines that run FROM the equator. Lines that are parallel TO the equator are the latitudes.