Question

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

Explanation:

Step1: Recall the definition of skew lines

Skew lines are non - parallel, non - intersecting lines that lie in different planes.

Step2: Analyze each option

• Option "They lie in different planes and will be parallel if a plane is drawn to contain both lines": If a plane can be drawn to contain both lines, they are not skew (since skew lines cannot be in the same plane). Also, if they were parallel, they would be coplanar (parallel lines are in the same plane).
• Option "They lie in different planes but will intersect if a plane is drawn to contain both lines": Skew lines do not intersect. If a plane could be drawn to contain both lines, they would be coplanar (not skew) and if they intersected, they would be intersecting lines (not skew).
• Option "They lie in the same plane but will never intersect": Lines in the same plane that do not intersect are parallel lines, not skew lines.
• Option "They lie in different planes and will never intersect": This matches the definition of skew lines.

Answer:

They lie in different planes and will never intersect.