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Chapter 2 Review Geometry Name:__________________________________________ Fill in the blank with the correct term. 1. Two angles that add up to 180. __________________ 2. Ray that divides an angle into two congruent angles. __________________ 3. A segment, line, ray or plane that intersects a segment at its midpoint. ________________ 4. The point right in the middle of a segment. __________________ 5. Two angles that add up to 90. __________________ 6. Two angles that make a straight line. __________________ 7. Angles that are right next to each other and share a common side. __________________ 8. Angles across from each other that are always equal. __________________ TERMS Complementary Angles Supplementary Angles Midpoint Adjacent Angles Segment Bisector Angle Bisector Linear Pair Vertical Angles M is the midpoint of each segment. Solve for x and find the indicated lengths. 9. 10. Equation: Equation: x =_______ EM = ______ MF= ______ x =_______ JM = ______ MK = ______ Find the midpoint between each pair of points using the Midpoint Formula. 12. 9, 2 and 5, 3 11. 10, 4 and 4, 8 Midpoint: ( , x1 x 2 y1 y 2 , 2 2 ) Midpoint: ( , ) Find the indicated lengths. 13. 14. 15.5 TS = _______ RS = _______ 15. AC = 50 cm 4½ CB = _______ AB = _______ AB = _______ BC = _______ Find the angle measurements using the bisector information given. BD bi sec ts ABC 16. YA bi sec ts XYZ m1 50 17. m2 _______ mABC _____ mXYZ 70 m1 ______ m2 ______ Given that BD is the bisector of ABC, write an equation and solve. 18. Equation: x = _______ 19. Equation: x = _______ mABD = _______ mDBC = _______ mABC = _______ mABD = _______ mABC = _______ 20. Complementary angles add to ________ 21. Supplementary angles add to ________ Find the measure of the complement and the supplement of each angle, if possible. 22. 30 23. 75 24. 150 complement - _________ complement - _________ complement - _________ supplement - _________ supplement - _________ supplement - _________ Find the measure of the given angle(s). 25. 26. 48 ° These angles add to ________ These angles add to ________ m1 = _________ m1 = _________ 27. 2 and the 20 angle are ___________ m1 = _________ m2 = _______ m3 = _______ Solve for x. 28. 29. 30. These angles add to ________ Equation: These angles add to ________ Equation: x = _______ x = _______ These angles add to ________ Equation: x = _______ Determine whether the angles are vertical angles, a linear pair, or neither. 31. 1 and 4 _______________________ 32. 1 and 5 _______________________ 33. 1 and 2 _______________________ 34. 3 and 4 _______________________ 35. 4 and 5 _______________________ 36. 2 and 3 _______________________ Find the measure of each numbered angle. 37. 38. 39. m1 = _____ m2 = _____ m1 = _____ m2 = _____ m3 = _____ m4 = _____ m3 = _____ m4 = _____ 40. 41. 42. These angles add to ________ These angles add to ________ These angles are _____________ Equation: Equation: Equation: x = _______ x = _______ w = _______ 29 m2 = _________ Solve for the variable. Use the diagram for the following questions. 43. An angle complementary to 2 _____ 44. An angle complementary to 4 _____ 45. An angle supplementary to EGC _____ 46. An angle supplementary to AGB _____ 47. A vertical angle with AGB _____ 48. A vertical angle with 4 ____ Underline the hypothesis and circle the conclusion of the if-then statement. 49. If two angles have the same measure, then the angles are congruent. 50. If the measure of an angle is 90˚, then the angle is a right angle. 51. If the sum of the measures of two angles is 180˚, then the angles are supplementary. Rewrite the statement in if-then form. 52. I will purchase a yearbook if it costs less than $20. 53. A dog with proper training will not misbehave. 54. Two angles that have the same measure are congruent angles. What law of logic is illustrated in the following statements? What can you conclude if the statements are true? 55. If you earn more than $14, you can buy a new CD. You earn $15. Law: Conclusion: 56. If the area of a square is 49 square inches, then the length of a side of the square is 7 inches. If the length of a side of a square is 7 inches, then the perimeter of the square is 28 inches. Law: Conclusion: 57. If the measure of an angle is between 0˚ and 90˚, then the angle is acute. The measure of an angle is 51˚. Law: Conclusion: Match each statement with the property that it illustrates. 58. ∠B ≅ ∠B A. Reflexive Property of Equality ̅̅̅̅ ≅ 𝑅𝑆 ̅̅̅̅, then 𝑅𝑆 ̅̅̅̅ ≅ 𝑃𝑄 ̅̅̅̅ 59. If 𝑃𝑄 B. Symmetric Property of Equality 60. If m ∠A = m ∠B and m ∠B = m ∠C, then m ∠A = m ∠C. C. Transitive Property of Equality ̅̅̅̅ and 𝑂𝑃 ̅̅̅̅ ≅ ̅̅̅̅ 61. If ̅̅̅̅̅ 𝑀𝑁 ≅ 𝑂𝑃 𝑄𝑅, then ̅̅̅̅̅ 𝑀𝑁 ≅ ̅̅̅̅ 𝑄𝑅 D. Reflexive Property of Congruence 62. m ∠1 = m ∠1 E. Symmetric Property of Congruence 63. If m ∠3 = m ∠4, then m ∠4 = m ∠3 F. Transitive Property of Congruence Name the property of equality that the statement illustrates. 64. If m ∠1 = m∠4, then m ∠1 - 30˚ = m ∠4 - 30˚ _____________________________________________ 65. If LM = NP, then 2•LM = 2•NP ________________________________________ 66. If XY = EF, then XY + 7 = EF + 7 ________________________________ 67. If CD = 4, then CD + 12 = 4 + 12 _________________________________ 68. In the figure at the right, ∠JKL ≅ ∠EDF, and ∠EDF ≅ ∠CDE. Complete the argument to show that ∠CDE ≅ ∠JKL. ∠JKL ≅ ∠EDF Given ∠EDF ≅ ∠CDE Given ∠JKL ≅ ∠CDE __________________ property of congruence ∠CDE ≅ ∠JKL __________________ property of congruence 69. In the diagram, m ∠1 + m ∠2 = 98˚, and m ∠1 = 42˚. Complete the argument to show that m ∠2 = 56˚. m ∠1 + m ∠2 = 98˚ Given m ∠1 = 42˚ Given 42˚ + m ∠2 = 98˚ ________________________ m ∠2 = 56˚ ________________________