Question

determine whether the lines are parallel, perpendicular, or neither.

1. l and n
2. l and m
3. l and n

use the diagram at the right.

1. name a pair of perpendicular lines.
2. name a pair of lines that appear parallel.
3. name a pair of skew lines.
4. name a line perpendicular to plane s.
5. suppose line l lies in plane s and intersects line p. what line must be perpendicular to l?

the drawing depicts a cricket cage with a rectangular top and bottom and small wooden “bars” for sides. describe any parts of the cage that suggest the geometric relationships.

1. a pair of parallel planes
2. a line perpendicular to a plane
3. a pair of parallel lines

Explanation:

Step1: Recall line - relationship definitions

Parallel lines never intersect, perpendicular lines intersect at a right - angle, and skew lines are non - coplanar and do not intersect.

Step2: Analyze line relationships in first set of diagrams

For 10. \(l\) and \(n\)

In the first diagram for 10, \(l\) and \(n\) are perpendicular as they intersect at a right - angle.

For 11. \(l\) and \(m\)

In the second diagram for 11, \(l\) and \(m\) are parallel as they are vertical and never intersect.

For 12. \(l\) and \(n\)

In the third diagram for 12, \(l\) and \(n\) are perpendicular as they intersect at a right - angle.

Step3: Analyze lines in the second diagram

For 13. Perpendicular lines

\(p\) and \(q\) are perpendicular as they intersect at a right - angle.

For 14. Parallel lines

\(q\) and \(r\) are parallel as they are in the same plane and do not intersect.

For 15. Skew lines

\(p\) and \(r\) are skew lines since \(p\) is not in the plane of \(r\) and they do not intersect.

For 16. Line perpendicular to plane \(S\)

Line \(p\) is perpendicular to plane \(S\) as it is at a right - angle to lines in the plane \(S\).

For 17. If \(l\) lies in \(S\) and intersects \(p\)

Since \(p\perp S\) and \(l\subset S\), then \(p\perp l\).

Step4: Analyze the cricket - cage

For 18. Parallel planes

The top and bottom of the cricket - cage are parallel planes.

For 19. Line perpendicular to a plane

The vertical wooden bars are lines perpendicular to the top and bottom planes of the cricket - cage.

For 20. Parallel lines

The horizontal wooden bars on the top or bottom of the cricket - cage are pairs of parallel lines.

Answer:

1. Perpendicular
2. Parallel
3. Perpendicular
4. \(p\) and \(q\)
5. \(q\) and \(r\)
6. \(p\) and \(r\)
7. \(p\)
8. \(p\)
9. The top and bottom of the cricket - cage
10. The vertical wooden bars
11. The horizontal wooden bars on the top or bottom of the cricket - cage