Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Analytic geometry wikipedia , lookup
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Perceived visual angle wikipedia , lookup
Line (geometry) wikipedia , lookup
Trigonometric functions wikipedia , lookup
Multilateration wikipedia , lookup
Chapter 2 Review Geometry Name:__________________________________________ Fill in the blank with the correct term. 1. Two angles that add up to 180. __________________ TERMS Complementary Angles Supplementary Angles Midpoint Adjacent Angles Segment Bisector Angle Bisector Linear Pair Vertical Angles 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. __________________ M is the midpoint of each segment. Write an equation, solve for x, and find the indicated lengths. 11. 12. 13. Equation: Equation: Equation: x =_______ EM = ______ MF= ______ x =_______ JM = ______ MK = ______ x x y y , Use the Midpoint Formula to find the midpoint coordinate for each pair of points. 2 2 14. 7, 2 and 5, 1 15. 10, 4 and 4, 8 ( , ) ( , x =_______ LM = ______ MN = ______ 16. 9, 2 and 5, 3 ) ( , Midpoint: Midpoint: Midpoint: Notice the bisector and corresponding tick marks. Find the indicated lengths. 18. 19. 20. AC = 50 cm 15.5 ) 4½ TS = _______ RS = _______ CB = _______ AB = _______ 21. Name the bisector of this angle.______ Name the congruent angles: _____________ AB = _______ BC = _______ Find the angle measurements using the bisector information given. Do NOT use a protractor for these questions! BD bi sec ts ABC 22. m1 50 m2 _______ mABC _____ YA bi sec ts XYZ 23. mXYZ 70 m1 ______ m2 ______ Given that BD is the bisector of ABC, write an ALGEBRAIC EQUATION and solve. 24. Equation: 25. Equation: x = _______ mABD = _______ mABC = _______ x = _______ mABD = _______ mDBC = _______ mABC = _______ Name the adjacent angles in each picture: 26. 27. Adjacent Angles: _______________________ 28. Adjacent Angles: _______________________ Adjacent Angles: _____________________________ 29. Complementary angles add to ________ Supplementary angles add to ________ Find the measure of the complement and the supplement of each angle. 30. 30 31. 75 32. 150 33. complement - _________ complement - _________ complement - _________ complement - _________ supplement - _________ supplement - _________ supplement - _________ supplement - _________ Find the measure of the given angle(s). 34. 35. These angles add to ________ m1 = _________ 36. These angles add to ________ m1 = _________ 2 and the 20 angle are ___________ m1 = _________ m2 = _______ m3 = _______ Given the picture, write an algebraic equation and solve for x. 37. 38. These angles add to ________ Equation: 179 39. These angles add to ________ Equation: These angles add to ________ Equation: x = _______ x = _______ x = _______ Determine whether the angles are vertical angles, a linear pair, or neither. 40. 1 and 4 _______________________ 41. 1 and 5 _______________________ 42. 1 and 2 _______________________ 43. 3 and 4 _______________________ 44. 4 and 5 _______________________ 45. 2 and 3 _______________________ Find the measure of each numbered angle. 46. 47. 48. 29 m2 = _________ m1 = _____ m2 = _____ m1 = _____ m2 = _____ m3 = _____ m4 = _____ m3 = _____ m4 = _____ Use the linear pair or vertical angles to write an ALGEBRAIC EQUATION and solve. 49. 50. 51. These angles add to ________ These angles add to ________ These angles are _____________ Equation: Equation: Equation: x = _______ x = _______ w = _______ Use the diagram for the following questions. 52. An angle complementary to 2 _____ 53. An angle complementary to 4 _____ 54. An angle supplementary to EGC _____ 55. An angle supplementary to AGB _____ 56. A vertical angle with AGB _____ 57. A vertical angle with 4 ____ Identify the hypothesis and conclusion of the if-then statement by underlining. 58. If two angles have the same measure, then the angles are congruent. 59. If the measure of an angle is 90˚, then the angle is a right angle. 60. If the sum of the measures of two angles is 180˚, then the angles are supplementary. Rewrite the statement in if-then form. 61. I will purchase a yearbook if it costs less than $20. 62. A dog with proper training will not misbehave. 63. 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? 64. If you earn more than $14, you can buy a new CD. You earn $15. Law: Conclusion: 65. 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: 66. 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. 67. ∠B ≅ ∠B A. Reflexive Property of Equality ̅̅̅̅ ≅ 𝑅𝑆 ̅̅̅̅, then 𝑅𝑆 ̅̅̅̅ ≅ 𝑃𝑄 ̅̅̅̅ 68. If 𝑃𝑄 B. Symmetric Property of Equality 69. If m ∠A = m ∠B and m ∠B = m ∠C, then m ∠A = m ∠C. C. Transitive Property of Equality ̅̅̅̅ and 𝑂𝑃 ̅̅̅̅ ≅ ̅̅̅̅ 70. If ̅̅̅̅̅ 𝑀𝑁 ≅ 𝑂𝑃 𝑄𝑅, then ̅̅̅̅̅ 𝑀𝑁 ≅ ̅̅̅̅ 𝑄𝑅 D. Reflexive Property of Congruence 71. m ∠1 = m ∠1 E. Symmetric Property of Congruence 72. If m ∠3 = m ∠4, then m ∠4 = m ∠3 F. Transitive Property of Congruence Name the property of equality that the statement illustrates. 73. If m ∠1 = m∠4, then m ∠1 - 30˚ = m ∠4 - 30˚ _____________________________________________ 74. If LM = NP, then 2•LM = 2•NP ________________________________________ 75. If XY = EF, then XY + 7 = EF + 7 ________________________________ 76. If CD = 4, then CD + 12 = 4 + 12 _________________________________ 77. In the diagram, AB + BC = 12, and BC = 3. Complete the argument to show that AB = 9. AB + BC = 12 Given BC = 3 Given AB + 3 = 12 _____________________ property of equality AB = 9 _____________________ property of equality 78. 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 79. 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˚ ________________________