1–4. Answers may vary. Samples are given. Tessellations GEOMETRY LESSON 12-6 Pages 670-672 Exercises 1–4. Answers may vary. Samples are given. 1. yes; translation; two rectangles 2. yes; translation; two and a rhombus with a flower in it 3. yes; translation; four rectangles in a square shape 4. no 5. yes 6. yes 7. no 8. no 9. no 10. no 11. rotational, reflectional, glide reflectional, and translational 12. rotational, point, reflectional, glide reflectional, and translational 13. rotational, reflectional, glide reflectional, and translational 14. rotational, point, and translational 15. rotational and reflectional s 12-6

16. rotational, point, and translational Tessellations GEOMETRY LESSON 12-6 16. rotational, point, and translational 17. 18. 19. 20–22. Answers may vary. Samples are given. 20. 21. 22. 12-6

Tessellations GEOMETRY LESSON 12-6 23. A regular polygon with more than 6 sides must have measures greater than 120, and at least 3 polygons must meet at each vertex. The sum of 3 or more with measures greater than 120 > 360. So the 3 regular polygons are 3-, 4-, and 6-sided, since their int. measures divide 360. 27. yes; 28–37. s 24. no 25. yes; 26. yes; 12-6

38. a–c. Drawings may vary. Sample: Tessellations GEOMETRY LESSON 12-6 38. a–c. Drawings may vary. Sample: d. Yes, ABCD tessellates; the sum of the measures of the of a quad. is 360. Copies of the quad. can be arranged so that the four share a vertex. The quad. fills the plane. s 39. Answers may vary. Sample: Draw ABC. Locate M, the mdpt. of AB, and N, the mdpt. of BC. Draw the images of ABC under 180° rotations about M and N. Draw the image of ABC under the translation that maps A to C. 2nd way: Draw ABC. Draw the reflection image of pt. C over AB, C . Now use the steps from Ex. 38 for quad. ACBC . 40. B 41. G 42. C 12-6

[1] correct answer with no explanation Tessellations GEOMETRY LESSON 12-6 43. [2] No; the int. of a pentagon measure 108. 108 is not a factor of 360, so a pentagon cannot tessellate the plane. (OR equivalent explanation) [1] correct answer with no explanation 44. [4] Line summetry: any vert. or horiz. line, a diag. line drawn through a square’s corners, or a line drawn through the bis. of a square’s side; rotational symmetry: 90° and point about any square’s center; translational: vertically or horizontally 1 unit; glide refl.: translate 1 unit and reflect through a line of symmetry (OR equivalent explanation) [3] 2 or 3 correct answers and explanations OR 3 or 4 correct answers with 2 or 3 incorrect explanations [2] 1 or 2 correct answers and explanations OR 2 or 3 correct answers with 1 or 2 incorrect explanations [1] incorrect explanations and answers s 12-6

Tessellations 45. (–2, –7) 46. (2, 7) 47. (2, –7) 48. (7, –2) GEOMETRY LESSON 12-6 45. (–2, –7) 46. (2, 7) 47. (2, –7) 48. (7, –2) 49. x2 + y2 = 36 50. (x – 1)2 + (y – 2)2 = 16 51. (x + 1)2 + y2 = 9 52. 9 53. 30 54. 7 12-6