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Practice CFor use with the lesson “Identify Points, Lines, and Planes”

In Exercises 1–16, use the diagram.

1. Give five other names for @##$ AB .

NK

E

B

DF

G

J

C

A

H M

L

2. Name four sets of three points that are collinear.

3. Name three points that are coplanar with both plane K and plane L.

4. Name all points that are not coplanar with points A, B, and H.

5. Give another name for }

CG .

6. Name all rays with endpoint G.

7. Name four pairs of opposite rays.

8. Give another name for ###$ FB .

9. Are points A, G, and N collinear?

10. Are points A, G, and N coplanar?

11. Are points C, D, and G collinear?

12. Are points C, D, and G coplanar?

13. Name the intersection of @##$ AB and @###$ MN .

14. Name the intersection of @##$ CD and plane ABH.

15. Name the intersection of plane K and plane L.

16. Name the intersection of @##$ EF and plane K.

Sketch the figure described.

17. Three lines with only two 18. Two planes that do not intersect points of intersection

19. Two rays that intersect at their endpoints 20. Two collinear rays that do not intersect

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You are given an equation of a line and a point. Use substitution to determine whether the point is on the line.

21. y 5 3x 1 7; A(2, 13) 22. y 5 4x 2 3; A(5, 17) 23. 2y 5 23x 2 9; A(21, 23)

24. 5x 1 4y 5 28; A(4, 22) 25. 6y 2 7x 5 8; A(6, 4) 26. 22x 2 9y 5 220; A(28, 4)

Graph the inequality on a number line. Tell whether the graph is a segment, a ray or rays, a point, or a line.

27. x ≥ 6 28. x ≤ 210 29. 25 ≤ x ≤ 3

30. x ≥ 4 or x ≤ 7 31. x ≥ 0 or x ≤ 22 32. x2 ≤ 0

In Exercises 33–35, use the following information.

Perspective Drawing A perspective drawing is drawn using vanishing points, as described in the text. The figure below is a perspective drawing of a garage.

33. Draw the lines necessary to locate the two vanishing points.

34. Using the two vanishing points, draw the lines necessary to show the hidden lines of the garage.

35. Using heavy dashed lines, draw the hidden lines of the garage.

Practice C continuedFor use with the lesson “Identify Points, Lines, and Planes”

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Lesson Identify Points, Lines, and Planes, continued28. a. four-legged stool; Possible explanation: The tips of the 4 legs are not coplanar. b. Possible explanation: The three-legged stool will not rock because the tips of its legs will always be coplanar. The four-legged stool may rock if the tips of its legs are not coplanar.

29. a. Yes, it has one vanishing point.

b.

c. Sample answer:

Practice Level C

1. @##$ BA , @##$ AG , @##$ GA , @##$ BG and @##$ GB 2. A, G, and B; C, G, and D; E, B, and F; M, G, and N

3. points M, G, and N

4. points C, D, E, F, and J 5. }

GC

6. ###$ GA , ###$ GB , ###$ GC , ###$ GD , ####$ GM , and ###$ GN

7. ###$ GA and ###$ GB , ###$ GC and ###$ GD , ####$ GM and ###$ GN , ###$ BE

and ###$ BF 8. ###$ FE 9. no 10. yes 11. yes

12. yes 13. point G 14. point G 15. @###$ MN

16. point B

17. Sample answer: 18. Sample answer:

19. Sample answer: 20. Sample answer:

21. yes 22. yes 23. yes 24. no

25. no 26. yes

27. 2022 4 6

6

8 10 12 14

28. 2428212

210

216 0

ray ray

29. 0 2 4222426

325 30. 10 2 3

4 7

4 5 6 7 8

segment segment

31. 0 2 4222426

022 32. 0

0

21 32223 2124

rays point

33.

34.

35.

Study Guide

1. Sample answer: @##$ DC and line n 2. }

EC 3. ###$ FE

4. B 5. F 6. ###$ DC

7. Sample answer: Mp

8. Sample answer: M

p

j

Real-Life Application

1. Cleveland, OH; Columbia, SC; Jacksonville, FL 2. Los Angeles, CA 3. 388 latitude and 778 longitude 4. South Carolina

Challenge Practice

1. Sample answer: Rays: ###$ DG , ###$ GD , ###$ FG , ###$ GF , ###$ FD , ###$ DF , ###$ DB , ###$ BD , ###$ DC , ###$ CD , ###$ CB , ###$ BC , ###$ CA , ###$ AC , ###$ AF , ###$ FA , ###$ EA , ###$ AE , ###$ ED , ###$ DE , ###$ DA , ###$ AD ; Opposite rays: ###$ FG and ###$ FD , ###$ ED and ###$ EA , ###$ CD and ###$ CB

2. Sample answer:

E

A

D

FB

G C

3. @##$ YT 4. point T 5. no; yes

6. TVW, XTW, and VWX 7. @##$ XY , @##$ ZY , @##$ TY

8. no 9. Yes. The given point satisfies each equation. 10. No. The given point does not satisfy each equation. 11. No. The given point does not satisfy each equation.

12. Yes. The given point satisfies each equation.

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