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:

1. Recall the definitions:

• Parallel lines: Coplanar and never intersect.
• Perpendicular lines: Intersect at 90 degrees.
• Skew lines: Non - coplanar, never intersect, and not parallel.
• Intersecting lines: Meet at a point.

1. Planes Q and R are parallel. Line a is on plane Q and line b is on plane R. So lines a and b are non - coplanar.

• They are not parallel because for lines to be parallel, they need to be coplanar (and have the same slope or direction in a geometric sense).
• They are not perpendicular as there is no indication of a 90 - degree intersection (and they are not coplanar to intersect at all).
• They will not intersect because they lie on parallel planes, and lines on parallel planes that are not coplanar do not intersect.
• Since they are non - coplanar, non - intersecting, and not parallel, they are skew lines.

Answer:

They are skew lines.