geo book 3.1 key

Properties or Parallel Lines GEOMETRY LESSON 3-1

Pages 118-121 Exercises

1. PQ and SR with transversal SQ; alt. int. s 2. PS and QR with transversal SQ; alt. int. s 3. PS and QR with transversal PQ; same-side int. s 4. PS and QR with transversal SR; corr. s

5.

1 and 2: corr. s 3 and 4: alt. int.

5 and 6: corr.

6.

s

s

s

1 and 2: same-side int. s 3 and 4: corr.

5 and 6: corr.

7.

8. alt. int.

s s

1 and 2: corr. s 3 and 4: same-side int. s 5 and 6: alt. int. s

9. a. 2

b. 1 c. corr.

10. a. Def. of b. Def. of right c. Corr. s of i lines are d. Subst.

e. Def. of right f. Def. of

.

Properties or Parallel Lines GEOMETRY LESSON 3-1

14. 70; 70, 110 11. m 1 = 75 because corr. s of || lines are ; 15. 25; 65 m 2 = 105 because same-side int. s of || 16. 20; 100, 80 lines are suppl.

17. m 1 = m 3 = m 6 = 12. m 1 = 120 because m 8 = m 9 = m 11 corr. s of || lines are ; = m 13 = m 15 = 52; m 2 = 60 because m 2=m 4=m 5= same-side int. s of || m 7 = m 10 = m 12 lines are suppl. = m 14 = 128 13. m 1 = 100 because same-side int. s of || lines are suppl.; m 2 = 70 because alt. int. s of || lines have = measure.

18. You must find the measure of one . All s that are vert., corr., or alt. int. to that will have that measure. All other s will be the suppl. of that measure.

19. two 20. four

21. two 22. four 23. 32

Properties or Parallel Lines GEOMETRY LESSON 3-1

24. x = 76, y = 37, v = 42, w = 25 25. x = 135, y = 45 26. The s labeled are corr. s and should be . If you solve 2x – 60 = 60 – 2x, you get x = 30. This would be impossible since 2x – 60 and 60 – 2x would equal 0.

27. Trans means across or over. A transversal cuts across other lines.

28. Answers may vary.

Sample: E illustrates corr. s ( 1 and 3, 2 and 4) and same-side int. s ( 1 and 2, 3 and 4); I illustrates alt. int. s ( 1 and 4, 2 and 3) and same-side int. s ( 1 and 3, 2 and 4).

29. a. alt. int.

s

b. He knew that alt. int.

30. a. 57 b. same-side int.

s

s

of || lines are

.

Properties or Parallel Lines GEOMETRY LESSON 3-1

31. a. If two lines are || and cut by a transversal, then same-side ext. s are suppl.

b. Given: a || b Prove: 4 and 5 are suppl.

1. a || b (Given) 2. m 5 + m 6 = 180 ( Add. Post.)

3. 4 6 (Corr. s are ) 4. m 5 + m 4 = 180 (Subst.)

5. 4 and 5 are suppl. (Def. of suppl.)

32. 1. a || b (Given) 2. 1 2 (Vert.

3. 2 3 (Corr.

4.

1

33. Never; the two planes do not intersect.

34. Sometimes; if they are ||.

35. Sometimes; they may be skew.

36. Sometimes; they may be ||.

37. D

38. G are .) s are .)

s

3 (Trans. Prop.)

39. D 40. I

Properties or Parallel Lines GEOMETRY LESSON 3-1

41. [2] a. First show that 1 7. Then show that 7 5. Finally, show that 1 5 (OR other valid solution plan). b.

1 7 because vert. s are .

7 5 because corr. s of || lines are . Finally, by the Trans. Prop. of , 1 5.

42. 121 43. 59 44. 29.5 45. (0.5, 7) 46. (–0.5, 3.5)

[1] incorrect sequence of steps OR incorrect logical argument

47. (3, 3)

48. add 4; 20, 24 49. multiply by –2; 16, –32 50. subtract 7; –5, –12