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Each line can either intersect the edge which is common to the two planes at some point or be parallel to it. If the two lines intersect the edge, but at different points, then the lines are skew. If only one of the lines intersects the edge, then again the lines are skew. If neither of them intersect, then the two lines are parallel to the same edge and so they are parallel to one another so not skew.
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Do skew lines always intersect?
Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.
Do skew lines intersect if they are in the same plane?
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.
What is the name of two lines in different planes that do not intersect and are not parallel?
skew lines
Are any two noncoplanar lines skew?
I guess they are. If they're parallel or intersecting, then they're coplanar.
Two lines that do not intersect and are in different planes?
They are skew lines. Two parallel lines must be in the same plane.
