Chapter 4 — Answers
Selected answers for Chapter 4: Congruence, 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 4 · Teacher’s answers: Chapter 4 · Complete key: Answers to Exercises PDF · Printed answers: appendices PDF
Lesson 1 (pages 134–138)
3. A and E.
5. B.
7. A(4, 3), C(−3, −4).
9. On the y-axis.
12. Two.
16. The fourth (IV).
19. The hummingbirds.
23. Point A.
27. A(4, 1), B(6, 6). AB = .
31. A(5, 2), A(15, 2).
35. (900, 200).
37. 250 mm.
41. or .
Lesson 2 (pages 141–144)
2. The vertices.
4. A 32-gon.
6. That they are congruent.
8. They are right angles (and equal).
11. Line segments AB and EF intersect two others but not at their endpoints.
12. △AEG.
17. CBEG.
25. An octagon (an 8-gon).
27. D.
31. H.
34. HBCFIE ↔︎ MNIEHK.
40. Convex.
45. No.
48. 21 square units.
53. No.
Lesson 3 (pages 148–150)
1. BF and BP.
3. ∠B.
5. SAS.
10. TR = AN.
11. ∠I = ∠G.
15. Two triangles congruent to a third triangle are congruent to each other.
17. All the angles are acute.
20. None of the sides are equal.
22. All three.
29. 35°.
31. They get larger.
34. About 5.9 cm.
38. Perpendicular lines form right angles.
41. ASA.
44. Both are pairs of opposite rays.
Lesson 4 (pages 153–155)
2. The midpoint of a line segment divides it into two equal segments.
7. Corresponding parts of congruent triangles are equal.
10. ASA.
17. If the angles in a linear pair are equal, then their sides are perpendicular.
19. Hexagons.
20. △ABX ≅ △CBX.
26. No. △BDC is larger than △ADB.
35. AB = 7, AC = 4, BC = .
37. △ABC and △DEF would coincide.
38. The x-coordinates are equal; the y-coordinates are opposites.
40. SAS.
44. Yes.
Lesson 5 (pages 159–162)
3. ∠ABD and ∠ADB.
4. BD.
6. No.
8. If two sides of a triangle are equal, the angles opposite them are equal.
12. That it has at least two equal sides.
21. Addition.
22. Betweenness of Rays Theorem.
23. Substitution.
28. They appear to be parallel.
30. ∠S = ∠B = 72°.
38. 92.2°.
39. Obtuse.
43. A pentagon.
44. Because its sides intersect in points other than their endpoints.
50. They seem to be congruent.
52. It seems to be equilateral (and equiangular).
p. 750
Lesson 6 (pages 165–167)
1. SSS.
2. Corresponding parts of congruent triangles are equal.
5. They are a linear pair.
10. Five.
11. No.
16. CA = CB and AD = BD.
18. SSS.
24. SAS.
29. ∠ADC = ∠CBA because they are corresponding parts of congruent triangles.
38. SSS.
40. OC bisects ∠AOB.
42. Because an angle has exactly one ray that bisects it (the corollary to the Protractor Postulate).
Lesson 7 (pages 172–175)
1. A compass.
2. Distances between pairs of points.
5. A line segment is bisected.
11. ∠2 is complementary to ∠1.
12. Copying an angle.
18. It means equally distant.
25. Addition.
26. Substitution.
36. SSS.
37. Height = 7.5 in; width = 10 in.
Review (pages 176–180)
2. Because they have the same size and shape (they can be made to coincide).
4. They are all equal.
8. Statement 4.
13. An equilateral triangle is equiangular.
15. Substitution.
17. 60°.
19. 120°.
21. 30°.
25. SSS.
29. 90°.
33. 45°.
38. (or ).
40. At (−5, 3).
46. Seven.
Algebra Review (page 182)
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11. or .
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19. or .
20. .
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25. .