Chapter 5 — Answers

Selected answers for Chapter 5: Inequalities, 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 5 · Teacher’s answers: Chapter 5 · Complete key: Answers to Exercises PDF · Printed answers: appendices PDF

Lesson 1 (pages 186–189)

1. Either $h>w$, $h=w$, or $h<w$.

6. The transitive property.

8. Multiplication.

11. Addition.

14. AB > BC.

15. Substitution.

20. ∠APB > ∠HPI.

22. ∠PIH < ∠PBA.

26. Transitive.

30. The “whole greater than part” theorem.

34. ∠A ≈ 83°, ∠B ≈ 56°, ∠C ≈ 41°.

37. 9 units.

41. That the line is “upright” (contains the center of the earth).

Lesson 2 (pages 192–194)

1. ∠BCY, ∠BAX, ∠CAD (∠YAD).

3. It gets smaller.

6. An exterior angle of a triangle is greater than either remote interior angle.

9. ∠2, ∠5, ∠8.

10. Two.

16. Two.

19. ∠ROS.

20. ∠ROA > ∠SRO and ∠ROA > ∠S.

25. No. It does not form a linear pair with an angle of the triangle.

26. 360°.

28. 180°.

32. A line segment has exactly one midpoint.

37. The “whole greater than part” theorem.

39. Two points determine a line.

41. The angles in a linear pair are supplementary.

43. An exterior angle of a triangle is greater than either remote interior angle.

Lesson 3 (pages 197–199)

3. Each is the converse of the other.

4. BC < AC.

8. ∠A > ∠B.

10. If two sides of a triangle are unequal, the angles opposite them are unequal in the same order.

14. ∠B.

18. ∠A ≈ 29°, ∠B ≈ 104°, ∠C ≈ 47°.

19. DE.

22. DF ≈ 4.5 cm, EF ≈ 5.4 cm.

23. ∠X > ∠Y.

30. ∠BDE.

34. BE bisects ∠ABC.

36. Yes. They are congruent by ASA.

42. FG < GH because both are sides of △FGH in which GH is the longest side.

45. An equilateral triangle is equiangular.

47. The “whole greater than part” theorem.

Lesson 4 (pages 202–204)

2. DP + PH > DH.

6. They are collinear.

7. Yes; 160 million miles.

10. PA + PB > 12, PA + PC > 12, and PB + PC > 12.

17. A, B, and C are not collinear.

19. AB + BC = AC.

24. An angle has exactly one line that bisects it.

27. Substitution.

28. If two angles of a triangle are unequal, the sides opposite them are unequal in the same order.

33. The sum of any two sides of a triangle is greater than the third side.

35. Substitution.

44. 5.5 m.

p. 751

Review (pages 206–209)

5. The “three possibilities” property.

7. Both dimensions are 2.5 in.

12. One angle has a measure of 179°, and the other two angles are each less than 1°.

16. The midpoint of a line segment divides it into two equal segments.

17. Reflexive.

20. If the angles in a linear pair are equal, their sides are perpendicular.

22. If two sides of a triangle are unequal, the angles opposite them are unequal in the same order.

24. Transitive.

26. The small angles each appear to be equal to 10°.

29. An exterior angle of a triangle is greater than either remote interior angle.

34. $n>2$.

37. One.

39. Yes.

41. SSS.

43. Betweenness of Rays Theorem.

Algebra Review (page 210)

1. $\dfrac{4}{5}$.

2. $\dfrac{3x}{8}$.

3. $\dfrac{1}{x}$.

4. $\dfrac{x+1}{2}$.

5. $\dfrac{4}{7}$.

6. $\dfrac{1}{3}$.

7. $\dfrac{1}{x-5}$.

8. $\dfrac{x}{y}$.

9. $\dfrac{x+3}{10}$.

10. $\dfrac{x-4}{x-6}$.

11. $\dfrac{4}{4x}$.

12. $\dfrac{x^3}{x^4}$.

13. $\dfrac{-3}{x-2}$.

14. $\dfrac{8}{12}$ and $\dfrac{9}{12}$.

15. $\dfrac{28}{7x}$ and $\dfrac{2}{7x}$.

16. $\dfrac{y}{xy}$ and $\dfrac{x}{xy}$.

17. $\dfrac{3x}{3x+6}$ and $\dfrac{2}{3x+6}$.

18. $\dfrac{5(x+1)}{(x-1)(x+1)}$ or $\dfrac{5x+5}{x^2-1}$ and $\dfrac{x}{(x-1)(x+1)}$ or $\dfrac{x}{x^2-1}$.

19. $\dfrac{x^2}{xyz}$ and $\dfrac{y^2}{xyz}$.