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 will intersect. they are skew lines. they are parallel lines. they are perpendicular lines.

Explanation:

• Intersecting lines: Intersecting lines lie on the same plane and cross at a point. Since lines \(a\) and \(b\) are on parallel planes \(Q\) and \(R\), they cannot intersect.
• Skew lines: Skew lines are non - parallel and non - intersecting lines that do not lie on the same plane. But the direction of the arrows (which represent the direction of the lines) is the same.
• Parallel lines: Parallel lines are coplanar lines that do not intersect. Although \(a\) and \(b\) are not on the same plane, in three - dimensional space, when two lines (on parallel planes) have the same direction (as indicated by the arrow directions in the figure), they are parallel.
• Perpendicular lines: Perpendicular lines intersect at a right angle (\(90^{\circ}\)). Since \(a\) and \(b\) do not intersect, they cannot be perpendicular.

Answer:

They are parallel lines.