Question

fill in the blank with || or ⊥ to make the statement true. 6. line p? line t. 7. line p? line q. 8. line t? line s. 9. line t? line q. determine whether the lines are parallel, perpendicular, or neither. 10. l and n 11. l and m 12. l and n use the diagram at the right. 13. name a pair of perpendicular lines. 14. name a pair of lines that appear parallel. 15. name a pair of skew lines. 16. name a line perpendicular to plane s. 17. 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. 18. a pair of parallel planes 19. a line perpendicular to a plane 20. a pair of parallel lines

Explanation:

Step1: Analyze line - line relationships

For 6 - 9, look at the angles formed between the lines in the diagrams. If the angle between two lines is 90 degrees, they are perpendicular (⊥), if they never intersect and are in the same plane, they are parallel (||).
For 10 - 12, check the right - angle markings (if any) to determine perpendicularity and the relative orientation to check for parallelism.
For 13 - 16, identify the lines based on the definitions of perpendicular, parallel, and skew lines and the relationship between lines and planes.
For 17, use the property that if a line lies in a plane and another line is perpendicular to the plane, it is perpendicular to all lines in the plane that it intersects.
For 18 - 20, consider the structure of the cricket cage to identify parallel planes, lines perpendicular to planes, and parallel lines.

Step2: Answer each question

1. From the diagram, line p ⊥ line t.
2. Line p || line q.
3. Line t || line s.
4. Line t ⊥ line q.
5. l and n are perpendicular (⊥).
6. l and m are parallel (||).
7. l and n are neither parallel nor perpendicular.
8. One pair of perpendicular lines could be p and q (answers may vary).
9. One pair of parallel lines could be q and s (answers may vary).
10. One pair of skew lines could be p and r (answers may vary).
11. Line p is perpendicular to plane S.
12. Line p must be perpendicular to l.
13. The top and bottom of the cricket cage are a pair of parallel planes.
14. The vertical bars of the cricket cage are lines perpendicular to the top and bottom planes.
15. The horizontal bars on the same side of the cricket cage are pairs of parallel lines (answers may vary).

Answer:

1. ⊥
2. ||
3. ||
4. ⊥
5. ⊥
6. ||
7. Neither
8. p and q (answers may vary)
9. q and s (answers may vary)
10. p and r (answers may vary)
11. p
12. p
13. Top and bottom of the cricket cage
14. Vertical bars of the cricket cage
15. Horizontal bars on the same side of the cricket cage (answers may vary)