By A. V. Pogorélov

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New Vocabulary adjacent angles vertical angles linear pair complementary angles supplementary angles perpendicular Angle Pairs Adjacent angles are two angles that lie in the same plane, have a common vertex and a common side, but no common interior points. Examples Nonexamples ∠ABC and ∠CBD ∠ABC and ∠ABD ∠ABC and ∠BCD Words C D A A C C C D D D B B A B B A shared interior no common vertex Vertical angles are two nonadjacent angles formed by two intersecting lines. Examples Nonexample " ∠AEB and ∠CED ∠AED and ∠BEC ∠AED and ∠BEC % Words A !

AFD 30. ∠EFB 36 Chapter 1 Tools of Geometry ! & " % # $ and YZ are opposite rays. YU bisects ∠ZYW, ALGEBRA In the figure, YX bisects ∠XYW. and YT 31. If m∠ZYU = 8p ‒ 10 and m∠UYW = 10p ‒ 20, find m∠ZYU. Y 12 X 32. If m∠1 = 5x + 10 and m∠2 = 8x ‒ 23, find m∠2. 33. If m∠1 = y and m∠XYW = 6y ‒ 24, find y. T 34. If m∠WYZ = 82 and m∠ZYU = 4r + 25, find r. 35. If m∠WYX = 2(12b + 7) and m∠ZYU = 9b ‒ 1, find m∠UYW. 36. If ∠ZYW is a right angle and m∠ZYU = 13a ‒ 7, find a. Z U W 37. PATTERN BLOCKS Pattern blocks can be arranged to fit in a circular pattern without leaving spaces.

H 7 ft 5 in. J 7 ft 6 in. Refer to the figure at the right. (Lesson 1-1) D 62. Name three collinear points. C 63. Name two planes that contain points B and C. 64. Name another point in plane DFA. F A 65. How many planes are shown? E G B TRAVEL The Hernandez family is driving from Portland, Oregon, to Seattle, Washington. They are using maps to navigate a route. Name the geometric term modeled by each object. (Lesson 1-1) 66. map 67. highway 68. city PREREQUISITE SKILL Evaluate each expression if a = 3, b = 8, and c = 2.

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