Yes.
No, not always. Skew lines are never coplanar, but parallel lines are.
They are always coplanar in Euclidean geometry.
Two lines with a transversal are always coplanar. By definition, a transversal is a line that intersects two or more lines in the same plane. Therefore, since the transversal and the two lines it intersects share the same plane, they are always coplanar.
Yes.
yes, two lines can be coplanar.
Parallel lines are ALWAYS coplanar.
Parallel lines are a specific type of coplanar lines that never intersect and are always the same distance apart. While all parallel lines are coplanar, not all coplanar lines are parallel; coplanar lines can also intersect at some point. Therefore, while the two concepts are related, they are not synonymous.
No. Skew lines are never coplanar. Stand in a cuboid room and consider the line where the opposite wall and the floor meet. Consider also the line where the walls behind you and to your right meet. Those two lines are not coplanar.
Yes. The two lines define a plane which they both belong to.
are two lines that are not parallel, coplanar, and do not intersect
No. If two lines intersect, then they're definitely coplanar.
No, two skew lines are not coplanar. Skew lines are defined as lines that do not intersect and are not parallel, meaning they do not lie in the same plane. Since they cannot be contained within a single plane, they are always found in different spatial positions relative to each other.