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Geometry Trimester 1 Final Review Name______________ Show all work!!! This review is worth points on your final exam. It must be turned in when you come to the exam. Under NO CIRCUMSTANCES will it be accepted late and you will not be allowed to go to your locker to get it. 1. Explain the difference between GH and GH . Draw pictures to go along with this explanation. 2. Explain the difference between JK and JK . 3. Explain whether MN and NM mean the same thing. What about ST and TS ? Pictures should accompany explanations. 4. Explain what it means for two rays to be opposite rays. Draw a picture to go along with this explanation. 5. Explain what it means to bisect something. 6. Explain what a counterexample is. 7. Explain what it means for two lines to be perpendicular to each other. What is the symbol for perpendicular? 8. If you have two parallel lines cut by a transversal, name 4 things you know: 1. 2. 3. 4. 9. What are the 5 ways to prove triangles congruent? 1. 2. 3. 4. 5. 10. What does CPCTC stand for? When can/should you use it? 11. What does it mean for a triangle to be isosceles? Draw an example. 12. What does it mean for a triangle to be equilateral? Draw an example. If the triangle is equilateral what else do we know about it? For problems 19-30, draw a picture (and label it) to go along with the given information. 13. M is the midpoint of GH . 14. TW bisects STU . 15. AED And CEB are acute, vertical angles. 16. XYSand SYZ form a linear pair. 17. QRT and TRS are complementary, 18. QRST is equiangular but not equilateral. adjacent angles.. 19. ABCDE is a concave pentagon. 20. ΔABC ΔDEC by SAS 21. j // k. 1 and 2 are alternate interior angles. 22. ΔJKL ΔMKL by HL 23. NH ST 24. M is the midpoint of LN . Find LN. 25. M is the midpoint of AC . Find AM. 26. BD bisects ABC . Find mABC . 27. BD bisects ABC . Find mABC . For problems 28-30, find the coordinates of the midpoint of AB and then find AB. 28. A(0, 2) 29. A(1, 4) 30. A(-4, -2) B(-3, 8) B(5, 1) B(3, -7) For problems 31 – 33, use the information to find the indicated measure. 31. Area = 504 in2 32. Circumference = 40π in Find the height h. Find the area. 33. Perimeter = 60 cm Find the length of each side. 5x+1 r 3x-3 34. Identify all of the pairs of corresponding angles in the diagram. 35. Identify all of the pairs of alternate interior angles in the diagram. 36. Identify all of the pairs of alternate exterior angles in the diagram. 37. Name 4 pairs of vertical angles. 38. Identify all of the pairs of same-side interior angles in the diagram. 39. Name 4 linear pairs. Find all the unknown angle measures in the diagram. 40. 1 41. 2 42. 3 43. 4 44. 5 45. 6 Decide if each argument is valid or invalid. If it is valid, tell what rule of logic it uses. If it is invalid, give a counterexample. 46. If today is Monday, then I go to school. Today is not Monday. Therefore, I do not go to school. 47. Jim or Mark dropped the pass. Mark did not drop the pass. Therefore, Jim dropped the pass. 48. If Amy hits a home run, then she is credited with an RBI. Amy is not credited with an RBI. Therefore, Amy did not hit a home run. 49. If you are at Osseo Senior High, then you are in Minnesota. If you are in Minnesota, then you are in the United States. Therefore, if you are in the United States, you are at Osseo Senior High. For the statement, rewrite it in if-then form. Then write the converse for the statement. Decide if each statement is true or false. If false, provide a counterexample. 50. A six-sided polygon is a regular hexagon. If – then: ______________________________________________________ True or False Converse: _______________________________________________________ True or False 51. A right angle is 90°. If – then: ______________________________________________________ True or False Converse: _______________________________________________________ True or False Find x. 52. 53. 54. In the diagram, RS ST . Find the value of x and y. 55. 56. Proofs 57. Given: Prove: Statements 58. Given: p //t; q // r Prove: 1 3 Statements 59. Reasons Reasons Given: j // k Prove: 1 is supplementary to 5 Statements Reasons j q 1 4 5 k 60. Given: p // r; 1 2 Prove: h // g Statements g h Reasons p 3 1 r 2 MN PQ, MQ NP Prove: ΔMNQ ΔPQN 61. Given: Statements 62. Reasons B Given: AD BE Prove: AD bisects BE AB DE B E Statements Reasons C A E 63. Given: T V SU TV Prove: ΔSTU ΔSVU Statements Reasons D 64. Given: B is the midpoint of AE . B is the midpoint of CD . Prove: D C Statements 65. Reasons Given: JT JR JM TR Prove: ΔTMJ ΔRMJ Statements Reasons