Chapter 3 — Answers
Selected answers for Chapter 3: Lines and Angles, transcribed from the book’s appendix. They are meant for checking your work, not for copying — the book prints answers to selected exercises only.
Back to Chapter 3 · Teacher’s answers: Chapter 3 · Complete key: Answers to Exercises PDF · Printed answers: appendices PDF
Lesson 1 (pages 80–82)
1. Subtraction.
2. Substitution.
10. Addition.
14. No number (because there is no number when multiplied by 0 that gives 6).
19. If and , then . If , then by substitution.
21. Substitution.
25. and .
26. .
28. .
32. Substitution.
38. Division.
41. A direct proof.
Lesson 2 (pages 86–90)
4. The definition of betweenness of points.
7. 52.
9. BC + CD = BD, or 5 + 6 = 11.
15. 92,760,000 mi.
17. 18.
20. 9 − 2 = 7.
26. A, −25; B, 15.
30. B.
35. AB + BC is greater than AC.
38. AC = AB + BC.
Lesson 3 (pages 93–97)
6. The definition of betweenness of rays.
8. Rays.
11. The coordinates.
13. Acute.
16. 15.
22. Obtuse.
25. 14.4°.
26. Yes.
29. 28.8°.
31. ∠SCP + ∠PCK = ∠SCK.
35. 27.
38. They are the same.
41. Betweenness of Rays Theorem.
44. 20°.
50. 360.
51. 15.
Lesson 4 (pages 100–104)
3. Figures that can be made to coincide (or fit exactly together).
7. Then it divides it into two equal segments.
9. Each is the converse of the other.
15. No.
19. 45°.
22. 67.5°.
26. The midpoint of a line segment divides it into two equal segments.
28. 1.5.
31. 2 cm.
32. (or about 6.28).
42. 180.
44. They are each 36°.
Lesson 5 (pages 107–109)
1. 90°.
4. 87°.
8. 30°.
9. 150°.
16. ∠DOW + ∠WOF = ∠DOF.
19. 27°.
26. Betweenness of Rays Theorem.
28. Substitution.
35. 75°.
37. ∠S seems to be 90° larger than ∠C.
42. They are supplementary.
Lesson 6 (pages 112–115)
1. Because they are vertical angles.
7. They are a linear pair and they are supplementary.
12. 80°.
14. They are vertical angles.
16. No.
23. Two.
26. 180°.
30. These angles are linear pairs; so they are supplementary.
36. Vertical angles are equal.
37. ∠3 = ∠1 + 90°.
45. 179°59′58.25″.
p. 749
Lesson 7 (pages 119–121)
1. Two angles are complementary if their sum is 90°.
4. Supplements of the same angle are equal.
6. If the angles in a linear pair are equal, then their sides are perpendicular.
10. Vertical angles are equal.
14. DH, AE, and, if perspective is taken into account, HG, EF.
17. They are a linear pair.
21. They are perpendicular.
24. ∠1 and ∠3 look like vertical angles, yet they are not equal.
30. ∠BOX, 25°; ∠BOY, 65°.
33. 180°.
37. They are perpendicular.
Review (pages 124–128)
1. Yes. E-F-H because 6.1 < 7.7 < 10.8.
5. .
8. The handle is perpendicular to the blade.
11. CE-CS-CD.
13. 41.5.
18. 110.
23. They would be perpendicular.
28. Any number is equal to itself.
34. ft.
38. ∠AOB = .
43. Hexagons.
46. Six.
50. 150.
53. 120 steps per minute.
56. 6,480 inches per minute.
Algebra Review (page 130)
1. .
2. .
3. .
4. .
5. .
6. .
7. .
8. .
9. .
10. .
11. .
12. .
13. .
14. .
15. .
16. .
17. .
18. .
19. .
20. .
21. −49.
22. .
23. .
24. .