Question

planes t and x are parallel. plane t contains line a. plane x contains line b. which best explains the relationship between lines a and b? they are skew and will never intersect. they are parallel and will never intersect. they are perpendicular and will intersect. they will intersect at two points.

Explanation:

1. Recall the definition of skew lines: lines that are not parallel, not intersecting, and lie in different planes.
2. Analyze the given information: Planes \( T \) and \( X \) are parallel. Line \( a \) is in plane \( T \), line \( b \) is in plane \( X \).
3. Evaluate each option:

• "They are parallel and will never intersect": For lines to be parallel, they need to be in the same plane (or parallel planes with the same direction). From the diagram, lines \( a \) and \( b \) have different directions (one is horizontal, one is vertical in their respective planes), so they are not parallel. Eliminate this.
• "They are perpendicular and will intersect": Perpendicular lines can intersect, but since the planes are parallel, lines in different parallel planes cannot intersect (as parallel planes never meet, so lines in them can't cross). Eliminate this.
• "They will intersect at two points": A line can intersect another line at most once. This is impossible. Eliminate this.
• "They are skew and will never intersect": Skew lines are non - parallel, non - intersecting, and in different planes. Since planes \( T \) and \( X \) are parallel (so lines in them can't intersect) and lines \( a \) and \( b \) are not parallel (different directions), they fit the definition of skew lines.

Answer:

They are skew and will never intersect.