Chapter 8 — Answers
Selected answers for Chapter 8: Transformations, 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 8 · Teacher’s answers: Chapter 8 · Complete key: Answers to Exercises PDF · Printed answers: appendices PDF
Lesson 1 (pages 300–304)
1. A translation.
3. A rotation.
6. A reflection.
16. Exercises 9, 11, and 14.
17. Each has a vertical line of symmetry.
20. Yes.
25. A translation.
28. They are parallelograms because they have two sides that are both parallel and equal.
31. The opposite sides of a parallelogram are equal.
36. Betweenness of Rays Theorem.
37. Substitution.
43. A dilation.
44. They seem to be twice as long.
52. A translation.
56. A rotation.
Lesson 2 (pages 308–311)
4. units.
5. It is the segment’s perpendicular bisector.
7. A rotation.
9. 180°.
14. Its image looks the same.
18. B.
22. A reflection.
24. Yes, because it is the composite of two reflections in intersecting lines.
27. C and E.
28. 120°.
30. No. The figure does not look exactly the same upside down.
32. E.
35. E.
37. A translation.
41. A rotation.
44. If a point is reflected through a line, the line is the perpendicular bisector of the segment connecting the point and its image.
46. Its magnitude.
48. SAS.
Lesson 3 (pages 314–316)
3. A reflection.
5. A glide reflection.
8. ∠PAB and ∠PCD.
10. The opposite sides of a parallelogram are equal.
14. A reflection.
17. The magnitude of the rotation.
18. The lines bisect these angles.
22. They are the perpendicular bisectors of these line segments.
25. Two figures are congruent if there is an isometry such that one figure is the image of the other.
27. D.
29. G.
35. No, because the two dogs are not mirror images of each other.
39. A translation and a reflection.
42. B′(14, 9), C′(9, 6).
43. .
46. M(11, 4), N(12, 5), P(8, 1).
Lesson 4 (pages 321–324)
1. Rotation (or point) symmetry.
6. It has reflection (line) symmetry with respect to a line through home plate and second base.
12. The point itself.
14. A line looks the same if it is rotated 180°.
16. A line has reflection symmetry because it can be reflected (folded) onto itself.
19. That rays OA and OD are opposite rays and that rays OB and OC are opposite rays.
22. In a plane, two points each equidistant from the endpoints of a line segment determine the perpendicular bisector of the line segment.
25. They bisect each other.
30. Translation.
33. 22.5°.
34. No.
36. 16.
38. The y-axis.
42. Even.
45. Because it can be translated (in various directions) and look exactly the same.
Review (pages 325–329)
6. No.
8. A glide reflection.
9. A rotation.
11. That it can be rotated so that it looks the same in three positions.
17. Yes.
20. A reflection.
24. Two figures are congruent if there is an isometry such that one figure is the image of the other.
29. A translation.
31. About 47°.
36. Because △ADC is the reflection image of △ABC.
37. It has reflection (line) symmetry with respect to line AC.
41. 45°.
47. No.