Question

consider the diagram. why are lines ac and rs skew lines? they lie in different planes and will never intersect. they lie in the same plane but will never intersect. they lie in different planes but will intersect if a plane is drawn to contain both lines. they lie in different planes and will be parallel if a plane is drawn to contain both lines.

Explanation:

To determine why lines \( AC \) and \( RS \) are skew lines, we recall the definition of skew lines: lines that lie in different planes and do not intersect and are not parallel.

• Analyze the first option: "They lie in different planes and will never intersect." This matches the definition of skew lines.
• The second option is incorrect because skew lines do not lie in the same plane (parallel or intersecting lines lie in the same plane).
• The third option is incorrect because skew lines never intersect, regardless of any plane drawn.
• The fourth option is incorrect because skew lines are not parallel, and drawing a plane to contain them won't make them parallel.

Answer:

A. They lie in different planes and will never intersect.