Question

planes q and r are parallel. lines a and b are shown on planes q and r, respectively. which statement is true about lines a and b? they are parallel lines. they are perpendicular lines. they are skew lines. they will intersect.

Explanation:

• Parallel lines lie in the same plane and never meet. But lines \(a\) and \(b\) are on different (parallel) planes.
• Perpendicular lines intersect at a right - angle. Since \(a\) and \(b\) are on parallel planes, they don't intersect.
• Skew lines are non - parallel, non - intersecting lines that lie on different planes. Lines \(a\) and \(b\) are on parallel (different) planes, not parallel (as their directions are not necessarily the same), and do not intersect.
• Intersecting lines meet at a point. Since planes \(Q\) and \(R\) are parallel, lines \(a\) (on \(Q\)) and \(b\) (on \(R\)) cannot intersect.

Answer:

They are skew lines.