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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.

Q: When are two lines in intersecting planes skew?

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Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.

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.

skew lines

I guess they are. If they're parallel or intersecting, then they're coplanar.

They are skew lines. Two parallel lines must be in the same plane.

Related questions

Two lines in two intersecting planes can be parallel, intersecting, or skew.

Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.

Two lines that are not parallel and do not intersect are skew. If the non-intersecting lines are in the same plane then they are parallel.

False. The angles can be formed by two skew lines intersecting a third line.

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.

Intersecting planes!

skew lines

I guess they are. If they're parallel or intersecting, then they're coplanar.

They are skew lines. Two parallel lines must be in the same plane.

One.

skew

CorrectParallel lines as well as intersecting lines must be coplanar (in Euclidean geometry not quite sure about hyperbolic geometry...).Lines in space which neither are coplanar nor intersecting are called "skew"