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 do not intersect. But lines \(a\) and \(b\) are on different parallel planes \(Q\) and \(R\), so they are not in the same plane.
• Perpendicular lines: intersect at a right - angle. Since \(a\) and \(b\) are on different parallel planes, they do not intersect.
• Skew lines: are non - parallel, non - intersecting lines that do not lie in the same plane. Lines \(a\) and \(b\) are on different parallel planes (\(Q\) and \(R\)), so they are not in the same plane, not parallel (as there is no information to suggest they have the same slope or direction in their respective planes in a parallel sense across planes), and do not intersect (because the planes are parallel).
• Intersecting lines: meet at a point. Since planes \(Q\) and \(R\) are parallel, lines \(a\) and \(b\) (one on each plane) cannot intersect.

Answer:

They are skew lines.