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:

Step1: Recall skew lines definition

Skew lines are non - parallel, non - intersecting, and lie on different planes.

Step2: Analyze each option

• Option 1: For lines to be parallel, they should be on the same plane (or parallel planes with same direction). Here, lines \(a\) and \(b\) are on parallel planes but their directions don't seem parallel (from the diagram), so they are not parallel.
• Option 2: Perpendicular lines meet at a right angle. Since lines \(a\) and \(b\) are on different parallel planes and don't intersect, they can't be perpendicular.
• Option 3: Lines \(a\) and \(b\) are on different parallel planes, they are not parallel and they don't intersect (as planes are parallel, lines on them can't intersect), so they satisfy the definition of skew lines.
• Option 4: Parallel planes never intersect, so lines on them (in different planes) can't intersect.

Answer:

They are skew lines. (The option "They are skew lines.")