8.1 Points, Lines, Planes, and Angles 461 Solution m m m m m m m 6 52° 8 and 6 are vertical angles. 5 128° 8 and 5 are supplementary angles. 7 128° 5 and 7 are vertical angles. 1 128° 1 and 7 are alternate exterior angles. 4 52° 4 and 6 are alternate interior angles. 2 52° 6 and 2 are corresponding angles. 3 128° 3 and 1 are vertical angles. = = = = = = = 7 Now try Exercise 71 In Example 7, the angles could have been determined in alternate ways. For example, we mentioned = m 1 128° because 1 and 7 are alternate exterior angles. We could have also stated that = m 1 128° because 1 and 5 are corresponding angles. Instructor Resources for Section 8.1 in MyLab Math • Objective-Level Videos 8.1 • Interactive Concept Video: Using Equations to Find Angle Measures • PowerPoint Lecture Slides 8.1 • MyLab Exercises and Assignments 8.1 Exercises Warm Up Exercises In Exercises 1–10, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. Two lines in the same plane that do not intersect are called ________ lines. Parallel 2. Two lines that do not lie in the same plane and do not intersect are called ________ lines. Skew 3. The union of two rays with a common endpoint is called a(n) ________. Angle 4. Two angles, the sum of whose measures is 90°, are called ________ angles. Complementary 5. Two angles, the sum of whose measures is 180°, are called ________ angles. Supplementary 6. An angle whose measure is 180° is called a(n) ________ angle. Straight 7. An angle whose measure is 90° is called a(n) ________ angle. Right 8. An angle whose measure is greater than 90° but less than 180° is called a(n) ________ angle. Obtuse 9. An angle whose measure is less than 90° is called a(n) ________ angle. Acute 10. When two straight lines intersect, the nonadjacent angles formed are called ________ angles. Vertical Practice the Skills In Exercises 11–18, identify the figure as a line, half line, ray, line segment, open line segment, or half open line segment. Denote the figure by its appropriate symbol. 11. A B Ray, hAB 12. B A Open line segment, AB 13. B A Ray, hBA 14. B A Half line, BA 15. B A Line segment, AB 16. B A Half open line segment, AB 17. B A Line, gAB 18. B A Half line, AB In Exercises 19–30, use the figure to determine the following. SECTION 8.1 C D A B E H F G I 19. h h AB DC > AD 20. > BD CB BC 21. < BD CB gBC 22. h FE FG < gEG 23. < BC CD BD 24. h h BG FE < gBF 25. hFC FI < hIC 26. h BC BA < hCA
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