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FALL FINAL EXAM REVIEW NAME______________________________________DATE_________________PER.______ GEOMETRY FALL SEMESTER REVIEW PART 1. A REVIEW OF ALGEBRA Find the correct answer for each of the following. 1. m = ____________ Solve for ‘m’: m – 7 = -13 + m 2. x = ____________ Solve for ‘x’: 12(x – 7) + 3(2x + 2) = 50x – 62 3. c = ____________ Solve fore ‘c’: 3 (15c + 10) = 12c – 9 5 Match each conditional statement with the algebraic property that would be used to prove the conclusion. NOTE: All answer choices will be used, none will be repeated. _____4. If 3x = 180, then x = 60. A. Symmetric Property _____5. If j = k and k = m, then j = m B. Reflexive Property _____6. If p, then p = p. C. Transitive Property _____7. If 3x – 2 = 7, then 3x = 9. D. Division Property _____8. If XY = QR, then QR = XY. E. Addition Property PART 2. GEOMETRY BASICS Match each of the following terms with its correct description. ________9. Point A. a point that divides a line segment exactly in half ________10. Line B. an exact location in space ________11. Plane C. has one endpoint and continues infinitely in one direction ________12. Coplanar Points D. points that lie in the same line ________13. Line Segment E. a set of points in a row that continues infinitely in two directions ________14. Ray F. a set of points containing two endpoints and all of the points between them ________15. Midpoint G. a flat surface that continues infinitely in all directions ________16. Collinear Points H. Points that lie on the same plane Using the figure below, name each of the following. 17. ____________ 18. ____________ 19. ____________ The intersection of M and L L A ray opposite DB A plane containing CE B C E D M A 20. ____________ The intersection of L and CE Find the indicated value. 21. x = _______________ If A is between X and Y, and XA = 3x, AY = 2x + 5, and XY = 60, find the value of ‘x’. (Draw a picture…it helps!) Find the indicated length. 22. FG = _______________ F is the midpoint of EG. If EF = 2x + 3 and EG = 6x – 3, find FG. PART 3. ANGLE BASICS Using the figure below, find the indicated measures. D A 23. mCED = __________ mFEC = 32, find mCED. E 24. x = __________ mCEA = (6x – 20), mAED = (3x + 18), and mCED = 151. Find the value of ‘x’. C F Use the figure below to answer the following questions. 25. ____________________ Name a pair of adjacent, complementary angles. 26. ____________________ Which angle is vertical to STR? 27. ____________________ The measure of PTR is twice the measure of NTP. Find the measure of both angles. 28. ____________________ Find x if mMTN = (3x - 2) and mNTP = (4x + 1). 29. ____________________ Find x if mNTP = (2x + 20) and mSTR = (3x + 15). N M P Q T S R In the figure below, BA and BC are opposite rays, and BE bisects ABD. 30. mABE = __________ If mABE = (6x + 2) and mDBE = (8x – 14), then find mABE. D E A B 31. mEBD = __________ If mABE = (12n – 8) and mABD = (22n – 11), then find mEBD. C Match each description with its corresponding term. Write its corresponding letter in the blank provided. ______32. An angle with a measure between 0 and 90. A. angle ______33. Angles that have equal measures. B. right angle ______34. An angle with a measure of 90. C. vertex ______35. A ray that divides an angle into two congruent angles. D. congruent angles ______36. An angle with a measure of 180 E. straight angle ______37. An angle with a measure between 90 and 180. F. angle bisector ______38. A figure formed by two rays that have the same endpoint. G. adjacent angles ______39. Angles that have a common vertex and side, but share no interior points. H. segment bisector ______40. A pair of angles with a sum of 180. I. acute angle ______41. Two non-adjacent angles formed by two intersecting lines. J. midpoint K. obtuse angle L. complementary angles M. supplementary angles N. vertical angles Find the indicated measures. 42. ____________________ Find the measures of two complementary angles, A & B, if mA = (7x + 4) and mB = (4x + 9). PART 4. CONDITIONALS & ALGEBRAIC PROOFS Find the correct answer for each of the following. 43. Hypothesis: If you complete your final exam reviews, then you will do well on your final. 44. Conclusion: If you exempt your second period final, then you still need to show up for class. 45. Negation: August is the hottest month. 46. Converse: If you eat your ice cream too fast, then you’ll get a brain freeze. 47. Inverse: If you vote for Ruben on the next American Idol episode, then he will win the competition. 48. Contrapositive: If you want to pass this class, then you will get your teacher some chocolate. PART 5: COORDINATE GEOMETRY Find the indicated value. 49. d = _______________ Find the distance between the points -6 and 5 on the number line. 50. d = _______________ Find the distance between the points A(-3, 5) and B(0, 1). Find the midpoint of the segment with the given endpoints. 51. m = _______________ (-7, 7) and (-9, 8) 52. m = _______________ (-3, 6) and (2, -8) PART 6. PARALLEL LINES & TRANSVERSALS Use the figure below for problems 53. – 58. Identify each angle pair and tell whether they are congruent or supplementary. 53.TYPE:____________________ or supplements? 54.TYPE:____________________ or or 4 and 5 supplements? 55.TYPE:____________________ 1 and 5 supplements? 2 and 8 1 2 3 4 5 6 7 8 56.TYPE:____________________ or supplements? 57.TYPE:____________________ or or 3 and 5 supplements? 58.TYPE:____________________ 6 and 7 6 and 8 supplements? Find the value of ‘x’ in each of the following. (2x – 3) 59.x = ____________ 135 (2x + 7) 60.x = ____________ 103 Find the indicated value(s). 61.x = ____________ Find the values of ‘x’ and ‘y’. (3y + 8) (4x + 9) y = ____________ (19x + 10) 62.x = ____________ Find the value of ‘x’. (4x – 10) 110 63.x = ____________ (3x – 50) Find the value of ‘x’. (2x – 5) 64. x = ____________ 2x (6x – 12) Find the value of ‘x’. Use the pyramid below to answer questions 65 and 66. M 65. _________________________ Name all pairs of parallel segments. 66. _________________________ Name a segment skew to AE. A PART 7: TRANSFORMATIONAL GEOMETRY Draw the indicated reflection of the polygon, and state the coordinates of its new vertices. 67. L’(________, ________) Reflect across y = x. N M’(________, ________) N’(________, ________) M O’(________, ________) Q P’(________, ________) Q’(________, ________) R’(________, ________) O P R L R D E Translate the image as indicated, then state the coordinates of its new vertices. 68. A’(________, ________) B’(________, ________) Translate 3 units down and 4 units right. A D B C C’(________, ________) D’(________, ________) E’(________, ________) H E G F F’(________, ________) G’(________, ________) H’(________, ________) Rotate each polygon as indicated, then state the coordinates of the new vertices. 69. Q’(______, ______) Rotate 90 counterclockwise. T R’(______, ______) S’(______, ______) S T’(______, ______) Q R Dilate each of the following figures as indicated, then state the coordinates of the new vertices. 70. A’(______, ______) Scale Factor: 2 B’(______, ______) C’(______, ______) B A C PART 8. TRIANGLE BASICS & CONGRUENT TRIANGLES Determine whether it is possible to form a triangle with the given lengths of sides. If yes, classify the triangle by SIDES. 71. YES or NO 5, 4, and 3 or NO 5, 10, and 15 or NO 10, 100, and 100 or NO 15, 15, and 15 Classify: 72. YES Classify: 73. YES Classify: 74. YES Classify: Find the value of ‘x’ in each of the following. 75.x = ____________ (x + 10) x (x + 20) 76.x = ____________ (x – 37) (x – 42) x Answer each of the following questions. Write your final answer in the blank provided. 77. _______________ If BOY GAL, then YB __?__. 78. _______________ If QRS LMN, then Q __?__. Determine whether the following pairs of triangles are congruent by SSS, SAS, ASA, or not congruent. 79. __________ 80. __________ 81. __________ Write in the statements with their corresponding reasons in each two-column proof below. 82. GIVEN: PO QR PO bisects QPR P PROVE: Q R STATEMENTS REASONS Q O R