Geometry Part 1 Unit 2 Test Review Name__________________Date___________ 1-12: If mAIB = 53 and mDIE = 46, fill in all angles on the picture and then fill in each blank. 1. mBIC = ______ 4. mGIH = ______ 2. mFIG = ______ 5. mEIF = ______ 3. mCID = ______ 6. mHIA = ______ 7. BID and __________ are a linear pair. C B D E A I H 8. HIG and __________ are vertical angles. F G 9. AIB and __________ are complimentary angles. 10. mDIE + mEIF = m__________. This is an example of the ________________________________ 11. AID and __________ are supplementary angles. 12. Is ray IH the bisector of AIG?__________ How do you know?________________________________ 13-18: Write the conclusion of each statement using the law of detachment or the law of syllogism. 13. If Tom does his homework, he will understand proofs. Tom did his homework last night! Conclusion:_________________________________________ Law: ________________________ 14. If John goes camping, then Lou will go. If Lou goes, then Cindy will go. John went camping! Conclusion:_________________________________________ Law: ________________________ 15. If two angles are vertical, then they are congruent. 1  2 Conclusion:_________________________________________ Law: ________________________ 16. If a number is a whole number, then it is an integer. If a number is an integer, then it is a rational number. Conclusion:_________________________________________ Law: ________________________ 17. If 2 angles are complementary, then the sum of their measures is 90. A and B are complementary. Conclusion:_________________________________________ Law: ________________________ 18. If an animal is a fish, then it can swim. Rufus can swim. Conclusion:_________________________________________ Law:_________________________ 19-21: Is the following conditional statement true? If true, write its converse. If the converse is true, then write the statement in biconditional form. 19. If the sum of the measures of 2 angles equals 180, then they are supplementary. 20. Converse: 21. Biconditional: ______________________________________________________. ______________________________________________________. T F T F 22-27: Use the given statement to answer each. Given: My teacher will be happy if I ace this test! 22. Rewrite it in if-then form.____________________________________________________________ 23. State the hypothesis._______________________________________________________________ 24. State the conclusion.________________________________________________________________ 25. State the converse._________________________________________________________________ 26. State the inverse.__________________________________________________________________ 27. State the contrapositive._____________________________________________________________ 28-31: Write the symbolic statement in words given p: C is an acute angle and q: mC is 30. 28. q  p ________________________________________________________________________ 29. ~q  ~p ________________________________________________________________________ 30. ~p ________________________________________________________________________ 31. ~p  ~q ________________________________________________________________________ 32-52: Justify each statement with a definition, property, postulate, or theorem. *(Draw a picture) 32. P  P _____________________________________ 33. If RS = TW, then TW = RS. _____________________________________ 34. If 5y = -20, then y = -4. _____________________________________ 35. 2(a + b) = 2a + 2b _____________________________________ 36. If 2x + y = 70, and y = 3x, then 2x + 3x = 70. _____________________________________ 37. If AB  CD and CD  EF , then AB  EF . _____________________________________ 38. If 2z – 5 = -3, then 2z = 2. _____________________________________ 39. If m1 + m2 = 180, then 1 and 2 are supplementary. _____________________________________ 40. If m1 = 90, then 1 is a right angle. _____________________________________ 41. If m1 = m2, then 1  2. _____________________________________ 42. If AB = CD and RS = TU, then AB + RS = CD + TU. _____________________________________ 43. If 1 and 2 are complementary, then m1 + m2 = 90. _____________________________________ 44. *If ER bisects DEF, then DER  REF _____________________________________ 45. *If B is between A and C, then AB + BC = AC. _____________________________________ 46. If 1 2 ,then 1  2. _____________________________________ 47. If 3and 4 are right angles, then 3  4. 48. If a  b, then 7 is a right angle. 49. If C D and D  E, then C  E. _____________________________________ a 7 8 _____________________________________ b _____________________________________ 50. If C  E, then mC = mE. _____________________________________ 51. If AB = CD and AB = EF, then CD = EF. _____________________________________ 52. If 1 2 , then 1 and 2 are supplementary. _____________________________________ 53-55: Construct a Venn diagram illustrating the following two statements: 53. Some triangles have acute angles. 54. All right angles are congruent. 55. No child likes spinach. 56-58: Two hundred people were asked what kind of literature they liked to read. They could choose among novels, poetry, and plays. Answer the questions based on the results in the Venn diagram shown. Novels 45 56. How many people said they like all three types of literature? 5 57. How many people like to read poetry? Poetry 6 58. How many people like novels and plays, but not poetry? 59-66: State True or False. If false, give a counterexample to the right of your blank below. 59. Three collinear points are contained in only one plane. ______________ 60. If 2 lines intersect, their intersection is a plane. ______________ 61. A line may lie in more than one plane. ______________ 62. If 2 angles are complementary, then they are adjacent. ______________ 63. 3 non-collinear points are contained in more than one plane. ______________ 64. The intersection of 2 planes is an infinite number of points. ______________ 65. 3 points are always collinear. ______________ 66. 2 points are always collinear. ______________ 67: Complete the algebraic proof with the correct statement or reason. Given: Prove: 8x – 10 = 2(x + 4) x=3 Statements Reasons a. 8x – 10 = 2(x + 4) a. _______________________________ b. _____________________ b. Distributive Property of Equality c. 6x - 10 = 8 c. _______________________________ d. 6x = 18 d. _______________________________ e. e. _______________________________ x=3 38 72 8 Plays 26 68-69: Write an equation and solve for x in each problem. 4x + 11 68. 3x + 1 69. 4x - 26 3x + 4 70: Know the following definitions, postulates, and statements and how to do problems with them:                    Angle Addition Postulate Angle Bisector Between Biconditional Complementary angles Compound Statement Conclusion Conditional Statement Congruent Conjecture Conjunction Contrapositive Converse Counterexample Deductive Reasoning Disjunction Hypothesis Inductive Reasoning Invalid                    Inverse Law of Detachment Law of Syllogism Linear Pair Midpoint Negation Perpendicular Lines Postulate Proof Reflexive Right Angle Segment Addition Postulate Symmetric Supplementary angles Theorem Transitive Truth Value Venn Diagram Vertical Angles