23. Answers may vary. Sample: Dürer may have thought that the printed pattern resembled a fishing net. 25. C 27. Miquela

29.
Image Long Description

31a.
Image Long Description

b.
Image Long Description

33. Answers may vary. Sample: for a tourist map showing locations of attractions 35. green 37. purple

46. D E = 31  mm , E F = 41  mm d e equals 31 , mm . comma . e f equals 41 , mm 47. m ∠ D = 60 , m ∠ E = 80 , m ∠ F = 40 m angle , d equals 60 , comma m angle , e equals 80 , comma m angle , f equals 40

48. Answers may vary. Sample:

49.

50.

51.

Lesson 1-2 pp. 11–19

Got It? 1a. Answers may vary. Sample: R Q ↔ , Q S ↔ modified r q with left right arrow above , comma . modified q s with left right arrow above b. Answers may vary. Sample: plane RVS, plane VQS c. N, Q, T d. N, T 2. No; they do not have the same endpoint. 3a. Answers may vary. Sample: plane BFE, plane BFG b. Postulate 1-3 says that two distinct planes intersect in exactly one line, so you only need two points to name the line of intersection, by Postulate 1-1.

4a.

b. Answers may vary. Sample: J M ↔ modified j m with left right arrow above

Lesson Check 1. Answers may vary. Sample: X R ↔ , R Y ↔ modified x r with left right arrow above , comma . modified r y with left right arrow above 2. R X → , R Y → r x vector , comma . r y vector 3. R S ↔ modified r s with left right arrow above 4. R S ¯ , S R ¯ r s bar , comma . s r bar 5. No; they have different endpoints and extend in opposite directions. 6. to show that the line extends in both directions 7. To name both, you need to identify two points on the ray or line. For a ray, you use a single-sided arrow that must point away from the endpoint. For a line, the two letters can be written in either order and a double-sided arrow appears above the letters. A line can also be named with a single lowercase letter, but a ray cannot.

Exercises 9. Answers may vary. Sample: plane EBG, plane BFG 11. E, B, F, G 13. R S → , S R → , S T → , T S → , T W → , W T → , T R → , R T → , W R → , R W → , W S → , S W ¯ r s vector , comma . s r vector , comma . s t vector , comma . t s vector , comma . t w vector , comma . w t vector , comma . t r vector , comma . r t vector , comma . w r vector , comma . r w vector , comma . w s vector , comma . s w bar 15. R S ↔ modified r s with left right arrow above 17. U V ↔ modified u v with left right arrow above 19. plane QUX, plane QUV 21. plane XTQ, plane XTS

23.

25.

27. coplanar 29. noncoplanar 31. noncoplanar

33.

35.

37.

39. Not always; A C → eh c vector contains B C → , b c vector , comma but they are not the same ray.

41. sometimes 43. sometimes 45. never

47.

Postulate 1-2

49.

Postulate 1-3

51. Answers may vary. Sample: 6:00 is the only “exact” time. Other times are about 1:38, 2:43, 3:49, 4:54, 5:59, 7:05, 8:11, 9:16, 10:22, 11:27, and 12:33.

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