Q: What are two lines that are not coplanar and do not intersect?

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No. If two lines intersect, then they're definitely coplanar.

a transversal

skewed lines

Coplanar lines that don't intersect are parallel. Lines that are not parallel and do not intersect are skew lines.

Two lines are coplanar iff they are parallel OR intersect.

Related questions

are two lines that are not parallel, coplanar, and do not intersect

No. If two lines intersect, then they're definitely coplanar.

Two coplanar lines that never intersect are called called parallel lines.

Coplanar lines that do not intersect are parallel. Non-coplanar lines that do not intersect are called skew lines.

parallel lines

Coplanar lines that do not intersect are called parallel lines.

transversal

a transversal

Parallel Lines or Skew Lines.

If they intersect or are parallel.

skewed lines

Coplanar lines can intersect an infinite amount of times.