1. **State the problem:** Determine the relationship between lines a and d based on the given diagram and options. 2. **Analyze the diagram:** - Line a is vertical inside plane N. - Line d is horizontal, passing through both planes N and M. - There is a right angle symbol where lines a and c meet, indicating perpendicularity between a and c. 3. **Recall definitions:** - **Parallel lines:** Lines in the same plane that never intersect. - **Perpendicular lines:** Lines that intersect at a right angle. - **Skew lines:** Lines that are not parallel and do not intersect because they are in different planes. - **Non-coplanar:** Lines that do not lie in the same plane. 4. **Determine if lines a and d are parallel:** - Line a is vertical in plane N. - Line d is horizontal and passes through both planes. - Since they are not in the same direction and line d crosses planes, they are not parallel. 5. **Determine if lines a and d are perpendicular:** - The right angle is between a and c, not a and d. - No indication that a and d intersect at a right angle. 6. **Determine if lines a and d are skew:** - Skew lines are non-coplanar and do not intersect. - Since line d passes through both planes and line a is in plane N, they may be in different planes and not intersect. 7. **Determine if lines a and d are non-coplanar:** - Non-coplanar means lines do not lie in the same plane. - Line a is in plane N. - Line d passes through both planes, so it is not confined to plane N. **Conclusion:** Lines a and d are **skew** because they are not parallel, do not intersect, and are in different planes. **Final answer:** Lines a and d are skew.