Question

use the diagram at the right. determine whether the lines are parallel, perpendicular, or neither.

1. p and q
2. q and s
3. and q
4. s and r

use the diagram at the right.

1. name a pair of skew lines.
2. name a pair of parallel lines.
3. name a pair of perpendicular lines.

consider each segment in the diagram at the right as part of a line. complete the statement.

1. wz and xy appear to be _?_.
2. xv and vu are _?_.
3. wx and tz are _?_.
4. xv is _? to plane stu.
5. plane tuz is parallel to plane _?_.

use the diagram of the state flag of texas shown at the right.

1. name four pairs of parallel lines on the flag.
2. name two pairs of perpendicular lines on the flag.
3. what parts of the diagram represent a line perpendicular to a plane?

Explanation:

Step1: Recall line - relationship definitions

Parallel lines are lines in the same plane that never intersect. Perpendicular lines are lines that intersect at a right - angle. Skew lines are non - coplanar lines that do not intersect.

Step2: Analyze each pair of lines in the given diagrams

For 6: Lines \(p\) and \(q\) intersect at a right - angle, so they are perpendicular.
For 7: Lines \(q\) and \(s\) are parallel as they are in the same plane and do not intersect.
For 8: (Missing line in the description, assume it's not relevant for now).
For 9: Lines \(s\) and \(r\) intersect at a non - right angle, so they are neither parallel nor perpendicular.
For 10: In the 3 - D figure, for example, line \(l\) and line \(n\) are skew lines (assuming they are non - coplanar and do not intersect).
For 11: In the 3 - D figure, line \(m\) and line \(l\) are parallel (assuming they are in the same plane and do not intersect).
For 12: In the 3 - D figure, line \(m\) and line \(n\) are perpendicular (assuming they intersect at a right - angle).
For 13: In the 3 - D figure, \(\overleftrightarrow{WZ}\) and \(\overleftrightarrow{XY}\) are parallel as they are opposite sides of a rectangular face of the cube - like figure.
For 14: In the 3 - D figure, \(\overleftrightarrow{XV}\) and \(\overleftrightarrow{VU}\) are perpendicular as they meet at a right - angle.
For 15: In the 3 - D figure, \(\overleftrightarrow{WX}\) and \(\overleftrightarrow{TZ}\) are skew lines as they are non - coplanar and do not intersect.
For 16: In the 3 - D figure, \(\overleftrightarrow{XV}\) is parallel to plane \(STU\) as it does not intersect the plane.
For 17: In the 3 - D figure, plane \(TUZ\) is parallel to plane \(VWX\) as they are opposite faces of the cube - like figure.
For 18: On the Texas flag, possible pairs of parallel lines: \(AB\) and \(GH\), \(BC\) and \(EH\), \(FG\) and \(AB\), \(DE\) and \(BC\) (assuming appropriate naming of line - segments on the flag).
For 19: On the Texas flag, possible pairs of perpendicular lines: \(AB\) and \(BC\), \(FG\) and \(GH\).
For 20: The flag - pole represents a line perpendicular to the plane of the flag.

Answer:

1. Perpendicular
2. Parallel
3. Neither
4. For example, \(l\) and \(n\) (in the 3 - D figure)
5. For example, \(m\) and \(l\) (in the 3 - D figure)
6. For example, \(m\) and \(n\) (in the 3 - D figure)
7. Parallel
8. Perpendicular
9. Skew
10. Parallel
11. \(VWX\)
12. \(AB\) and \(GH\), \(BC\) and \(EH\), \(FG\) and \(AB\), \(DE\) and \(BC\)
13. \(AB\) and \(BC\), \(FG\) and \(GH\)
14. The flag - pole.