Pre-AP Geometry Chapter 2 Test Review Important Vocabulary: Conditional Converse Hypothesis Conclusion Segment Addition
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1 1 Pre-AP Geometry Chapter 2 Test Review Important Vocabulary: Conditional Converse Hypothesis Conclusion Segment Addition Midpoint Postulate Right Angle Opposite Rays Angle Bisector Angle Addition Complementary Adjacent Angles Postulate Angles Supplementary Perpendicular Linear Pair Vertical Angles Vertical Angle Linear pair Angles Lines Theorem Postulate Bisect Geometry Proof Reflexive Symmetric Addition Subtraction Property Multiplication Division Transitive Substitution Commutative Associative Property Property Property Property Combining Like Distributive Truth Value Inverse Contrapositive Negation Terms Property Bi-conditional Law of Law of Straight Angle Midpoint Deductive Detachment Syllogism Theorem Reasoning Definition Two-Way Table Union Intersection Independence Conditional Probability Standard/Goals: A.1.a.: I can apply properties such as: commutative, associative, identity, inverse, and substitution to simplify algebraic expressions. A.1.f.: I can find the probability of a simple event. C.1.a.: I can use definitions, basic postulates, and theorems about points, segments, lines, angles, and planes to write proofs. C.1.b.: o I can use inductive reasoning to make conjectures and use deductive reasoning to arrive at valid conclusions. o I can identify and write conditional statements and use these statements to form conclusions. C.1.c.: I can identify and write conditional or bi-conditional statements along with the converse, inverse, and contrapositive of a conditional statement and use these statements to form conclusions. C.1.e.: I can read and write different types and formats of proofs including two-column, flowchart, and paragraph proofs. D.1.b.: I can identify vertical, adjacent, complementary, and supplementary angle pairs and use them to solve problems. S.CP.1: I can define the union, intersection and complements of events in the context of probability. S.CP.2.: I can determine if two events are independent or not. S.CP.4.: I can use a two-way table involving categories to determine probabilities. S.CP.5.: I can recognize the concepts of conditional probabilities and independence in everyday situations. S.CP.6.: I can calculate a conditional probability and interpret the result in the context of the given problem. S.CP.7.: I can use the General Addition rule for both mutually exclusive and non-mutually exclusive events. S.CP.8(+): I can use the General Multiplication rule for events that are not independent. #1. What is the probability of rolling a 3 or 4 on a number cube and randomly drawing the 4 of spades from a deck of cards?
2 2 #2. In one class, 25% of the students received an A on the last test and 33% of the students received a B. What is the probability that a randomly chosen student received an A or a B? #3. What is the probability of rolling a 3 or a number less than 5 on a number cube? #4. You win 4 out of every 10 races that you run. Your friend wins 5 out of every 9 swimming competitions she enters. What is the probability of you both winning the next events? #5. What is the probability of rolling TWO 1 s if you roll a pair of dice? #6. What is the probability of drawing a KING or a DIAMOND from a standard deck of cards? #7. What is the probability of rolling a pair of dice and NOT rolling a 2 or a 3? Use the following to answer the next FOUR questions: Goals Frequency #8. How many games did the team play? #9. What is the relative frequency of games with 1 goal scored? #10. What is the probability that the team scored 2 or more goals? #11. Which expression can be used to determine the probability of scoring fewer than 3 goals?
3 3 The table below shows the number of participants at a charity event who walked or ran, and who wore a red t-shirt or a blue t-shirt. Use the table for the next FIVE QUESTIONS: BLUE T-shirt RED T-shirt TOTALS Walk Run Totals #12. What is the probability that a randomly chosen participant ran AND wore a red t-shirt? #13. What is the probability that a randomly chosen participant walked AND wore a blue t-shirt? #14. What is the P (walked wore a red t-shirt)? #15. What is the probability that a randomly chosen walker wore a red t-shirt? #16. What is the probability that a randomly chosen participant did NOT run? #17. A teacher who is a club sponsor must choose five students from a class of 27 to go present to the local chamber of commerce. In how many ways can the teacher select the students? #18. A teacher who is a club sponsor must choose five students from a class of 27 to go present to the local chamber of commerce. One will run the laptop/projector; one will make the large presentation poster, and one will be the spokesperson. In how many ways can the teacher select the students?
4 4 Consider the following statement: If you are a quarterback, then you play football. Write a statement for each of the following and state whether each statement is true or false. #19. Converse: #20. Inverse: #21. Contrapositive: #22. Is the original conditional TRUE or FALSE? If its true, then which of the above statements that you wrote would be also be true and would be the logical equivalent to the original conditional? GIVEN: and intersect at point F; m<afb = 70 degrees, bisects <BFD Find the following: #23. m<dfc #24. m<afb #25. m<afe #26. m<efd #27. m<afc #28. m<cfe #29. Consider the following: Dan says two things: #1. If I get the promotion at work, I will take my family out for a nice dinner. #2. If I take my family out for a nice dinner, I will take them to Guthrie s restaurant. Assume that Dan does what he says he will do and that that he does NOT take his family to Guthrie s, what can possibly be concluded? #29. <M and <N are supplementary angles. If m<n = p degrees, when write the measures of <M in terms of p. #30. <B and <Z are supplementary. If <B is 19 more than double the complement of <Z, find the angles
5 5 State the property that justifies each statement. #31. If 3(4 + x) = 18, then x = 18. #32. <JKM = <JKM #33. AB + BC = AC Use the figure above for the next TWO questions: #34. If B is a midpoint, then AB = ½ AC. #35. If B is a midpoint, then BA = BD. #36. If <5 and <6 are complementary, then <5 + <6 = 90. #37. If <7 + <8 = 180, then <7 and <8 are supplementary. #38. If <7 & <8 are a linear pair, then <7 and <8 are supplementary angles. Use the figure to the right for the next FOUR questions. #39. If <BFD is bisected by ray FC, then <BFC = <CFD. #40. If <BFD is bisected by ray FC, then <BFC = ½ <BFD. #41. <AFB + <BFC = <AFC. #42. If <AFB and <EFD are vertical angles, then <AFB = <EFD. #43. If 5x + 2y = 17 and y = 7, then 5x + 14 = 17 #44. If 4x = y and y = 10, then 4x = 10. #45. If x + 5 = 18, then 18 = x + 5. #46. A + W = W + A
6 6 #47. GIVEN: K is the midpoint of JL; JI = ½ JL PROVE: JI = LK #1. K is the midpoint of JL; JI = ½ JL #1. Given #2. ½ JL = LK #2. #3. JI = LK #3. #48. GIVEN: PR = ST; S is the midpoint of RT PROVE: PR = RS #1. PR = ST; S is the midpoint of RT #1. Given #2. RS = ST #2. #3. PR = RS #3. #49. GIVEN: AC = BD PROVE: AB = CD #1. AC = BD #1. Given #2. AB + BC = AC; BC + CD = BD #2. #3. AB = CD #3.
7 7 #50. GIVEN: <6 & <7 are supplementary PROVE: <5 = <7 #1. <6 & <7 are supplementary #1. Given #2. <6 + <7 = 180 #2. #3. <5 and <6 are a linear pair #3. #4. <5 and <6 are supplementary #4. #5. <5 + <6 = 180 #5. #6. <5 = <7 #6. #51. GIVEN: <5 = <6 PROVE: <5 & <7 are supplementary #1. <5 = <6 #1. Given #2. <6 and <7 are a linear pair #2. #3. <6 and <7 are supplementary #3. #4. <6 + <7 = 180 #4. #5. <5 + <7 = 180 #5. #6. <5 and <7 are supplementary #6.
8 8 #52. GIVEN: AB = 3x + 15, AC = 90, BC = 5x 5 PROVE: BC = 45 #1. AB = 3x + 15, AC = 90, BC = 5x 5 #1. Given #2. AB + BC = AC #2. #3. 3x x 5 = 90 #3. #4. 8x + 10 = 90 #4. #5. 8x = 80 #5. #6. x = 10 #6. #7. BC = 45 #7. #53. GIVEN: <8 & <7 are complementary PROVE: #1. <8 & <7 are complementary #1. Given #2. <8 + <7 = 90 #2. #3. <8 + <7 = <XYZ #3. #4. <XYZ = 90 #4. #5. <XYZ is a right angle #5. #6. #6.
9 9 #54. GIVEN: PROVE: <8 & <7 are complementary #1. #1. Given #2. <XYZ is a right angle #2. #3. <XYZ = 90 #3. #4. <8 + <7 = <XYZ #4. #5. <8 + <7 = 90 #5. #6. <8 and <7 are complementary #6. #55. GIVEN: bisects <XMZ PROVE: <6 = <3 #1. bisects <XMZ #1. #2. <6 and <4 are vertical angles #2. #3. <6 = <4 #3. #4. <4 = <3 #4. #5. <6 = <3 #5.
10 10 #56. GIVEN: bisects <XMZ PROVE: <6 = ½ <XMZ #1. bisects <XMZ #1. Given #2. <6 and <4 are vertical angles #2. #3. <6 = <4 #3. #4. <4 = ½ <XMZ #4. #5. <6 = ½ <XMZ #5. #57. GIVEN: <3 = 3x + 14, <4 = 5x 38 PROVE: <3 = 92 #1. <3 = 3x + 14, <4 = 5x 38 #1. Given #2. <3 and <4 are vertical angles #2. #3. <3 = <4 #3. #4. 3x + 14 = 5x 38 #4. #5. 14 = 2x 38 #5. #6. 52 = 2x #6. #7. x = 26 #7. #8. <3 = 92 #8. #58. GIVEN: <5 = <6 PROVE: <6 = <7 #1. <5 = <6 #1. Given #2. <5 and <7 are vertical #2. angles #3. <5 = <7 #3. #4. <6 = <7 #4.
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