a transversal
Usually, a transversal is a line that intersects two (or more) parallel lines. In that case the lines and the transversal are coplanar. However, a transversal does not have to intersect parallel lines. And in that case, the lines need not be coplanar. Here's one way to visualise the latter situation. Stand in a cuboid room. Line one = the edge joining the wall opposite you to the ceiling. Line two = the edge joining the wall on your right to the floor. Transvesal = the edge joining the opposite wall to the wall on your right. The transversal meets both the two lines but lines 1 and 2 are not coplanar.
transversal
corresponding angles
Two pairs of alternate opposite angles
transversal
a transversal
Normally, yes. A transversal contemplates crossing two (normally parallel) lines in conversations about two dimensional space and the relationship of certain angles. If you are talking about three dimensions, all bets are off. Two skewed lines in three dimensional space could would have a line that connects them but none of them would be coplanar.
A transversal.
They are always coplanar in Euclidean geometry.
Alternate Interior Angles
Transversal
Usually, a transversal is a line that intersects two (or more) parallel lines. In that case the lines and the transversal are coplanar. However, a transversal does not have to intersect parallel lines. And in that case, the lines need not be coplanar. Here's one way to visualise the latter situation. Stand in a cuboid room. Line one = the edge joining the wall opposite you to the ceiling. Line two = the edge joining the wall on your right to the floor. Transvesal = the edge joining the opposite wall to the wall on your right. The transversal meets both the two lines but lines 1 and 2 are not coplanar.
transversal
corresponding angles
Two pairs of alternate opposite angles
A transversal is simply any line that passes through two or more coplanar lines each at different points. So picture, if you will, two lines that are clearly not parallel. I can easily construct a transversal that passes through them. HOWEVER, if two parallel lines are intersected by a transversal, then the corresponding angles are congruent. This is called the transversal postulate. If the corresponding angles are congruent, than the lines are parallel. This is the converse of the first postulate. So, the answer to your question is NO, unless the corresponding angles are congruent.