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Name ___________________________ Chapter 2 Logic & Proof Test Review Rewrite the following statements as a conditional, then state the hypothesis and conclusion. 1. Whenever I think about home, I get misty-eyed. Conditional __________________________________________________________________ Hypothesis: __________________________Conclusion ____________________________ 2. If it rains tomorrow, then I will use my umbrella. Converse___________________________________________________________ Inverse_____________________________________________________________ Contrapositive________________________________________________________ 3. If m A = 90°, then A is a right angle. T or F Converse____________________________________________________________ T or F Inverse______________________________________________________________ T of F Contrapositive_________________________________________________________ 4. Write a true conditional statement from the following: Monday is a weekday. ______________________________________________________________________. Use inductive reasoning to complete the following patterns (5-7): 5. 3, 7, 11, 15, ______ 6. 7. -3, 6, -12, 24, _____ ______, ______ make a conjecture about this pattern ________________________ _____________________________________________________ 8. Complete the conjecture “The product of two negative numbers is ______________________”. Determine if the each conjecture is true. If not write a counterexample for each (9-11). 9. If 2x + 3 = 15, then x = 6. _____________________________________________ 10. If BD bisects <ABC, then m<ABD = m<CBD.____________________________________ 11. If n is an integer, then –n is positive.____________________________________________ 12. Rewrite the statements so that they are in a logical order and reach a conclusion. a. If Suzie Shopper gets fat, then her dress will not fit. b. If Suzie Shopper eats too much, then she will get fat. c. If Suzie Shopper needs a new dress, then she will go to dinner at a nice restaurant. d. If her dress does not fit, then Suzie Shopper will need to exercise. e. If Suzie Shopper goes to the store, then Suzie will buy shoes. f. If Suzie Shopper buys shoes, then Suzie Shopper will need a new dress. g. If Suzie goes to dinner at a nice restaurant, then Suzie Shopper will eat too much. Correct order: State the letters only. __________________________ Conclusion: _____________________________________________________________________ 13. Determine if the conjecture is valid by the Law of Syllogism: Given: If you fly from Texas to California, you travel from the central to the Pacific time zone. If you travel from the central to the Pacific time zone, then you gain two hours. Conjecture: If you fly from Texas to California, then you gain two hours. Valid or invalid ? 14. Determine if the conjecture is valid by the Law of Detachment: Given: If you want to go on a field trip, you must have a signed permission slip. Sophie has a signed permission slip. Conjecture: Sophie wants to go on a field trip. Valid or invalid ? Rewrite each definition or statement as a biconditional (15-16). 15. A triangle with no sides equal is a scalene triangle.___________________________________ 16. A circle is a set of points in a plane a given distance from the center.______________________ 17. Logic Puzzle: It is a three-digit odd number. It is less than 200. Each of the digits is different. The sum of its digits is 17. The ones digit is greater than 7. The number is __________ 18. Three little pigs, who each lived in a different type of house, handed out treats for Halloween. Use the clues to figure out which pig lived in each house and what type of treat each pig handed out. A. Petey Pig did not hand out popcorn. B. Pippin Pig does not live the wood house. C. The pig that lives in the straw house, handed out popcorn. D. Petunia Pig handed out apples E. The pig who handed out chocolate, does not live in the brick house. 19. The five things that can be used as reasons in a proof are: 20. If the pattern indicated below is continued, what would be the total number of cubes in the next stage of the pattern? Answers: 1. If I think about home, then I will get misty-eyed. H-I think about home C-I will get misty-eyed. 2. Con-If I use my umbrella, then it will rain tomorrow. In-If it doesn’t rain tomorrow, then I won’t use my umbrella. Cont-If I don’t use my umbrella, then it won’t rain tomorrow. 3. Con-If <A is a right, angle, then m<A=90. True In- If m<A≠90, then <A is not a right angle. True Cont- If <A is not a right angle, then m<A≠90. True 4. If it is Monday, then it is a weekday. 5. 19 6. , 7-sided figure 7. -48 ; each term is double the previous term with alternating signs. 8. Positive 9. True 10. True 11. If n=4, then -4 is not positive. 12. e,f,c,g,b,a,d ; If Suzie Shopper goes to the store, then she will need to exercise. 13. Valid 14. Invalid 15. A triangle is scalene if and only if it has no equal sides. 16. A set of points in a plane is a circle if and only if they are a given distance from the center. 17. 179 18. Petey, chocolate-wood; Pippin, popcorn-straw; Petunia,apples-brick 19. Definitions, postulates, theorems, given, algebra properties 20. 64 21. e,a,b,c 22. B,d,e,c,a,c 23.b,c,e,d,a,c Justifications: 1. Segment add. 2. Def.midpoint 3. Def. midpoint 4. Def. <s 5. Transitive prop. 6. Subtraction prop. 7. Def.supplementary <s 8. Reflexive prop. 9. Angle add. Post. 10. Symmetric prop. 11. Def. vertical <s 12. Def.compl.<s 13. Transitive prop. 14. Substitution prop. 15. Def. midpt. 16.def. supple.<s 17. Def. right < 18. Def.obtuse< 19. Reflexive prop. 20. All right <s are 21. Def. <s 22.transitive prop. 23. Subtraction prop. 24. Segment add. 25. All right <s 26. Def. right < 27. Division 28. Def. obtuse < 29. Def. angle bisector 30. Linear pr. Th. 31. Distributive prop. 32. Division prop. 33. Addition prop. Proofs: Complete each proof using the choices below each 2-column proof (some may be used more than once) : 21. Statements Reasons 3n + 25 = 9n -5 25 = 6n - 5 30 = 6n 5=n a. subtraction b. addition c. division d. multiplication e. given f. substitution 22. Given: 2 3 Prove: 1 and 3 are supplementary 1 2 Statements 3 Reasons 2 3 m2 m3 1 and 2 are supplementary m 1 + m 2 =180º m 1 + m 3 =180º 1 and 3 are supplementary a. substitution b. given c. definition of supplementary angles d. definition of congruent angles e. linear pair theorem f. reflexive property 23. Given: 1 and 2 are complementary Prove: 2 and 3 are complementary 1 2 3 Statements 1 and 2 are complementary m 1 + m 2 =90º 1 3 m1 m3 m 3 + m 2 =90º 2 and 3 are complementary a. substitution b. given c. definition of complementary angles d. definition of congruent angles e. vertical angles theorem f. reflexive property Reasons Justify each statement with a postulate, theorem, definition, or algebra property: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. If point X is between points C and D, then CX + XD = CD. If point A is between C and D where CA AD, then A is the midpoint of CD. If A is the midpoint of CD, then CA = ½ (CD). If mA = mD, then A D. If AB XY and XY MP, then AB MP. If AB + CD = CD + XY, then AB = XY. If 1 and 2 are supplementary, then m1 + m2 = 180. If XY MN, then XY MN. If X is in the interior of CPD, then mCPX + mXPD= mCPD. If ABC XYZ, then XYZ ABC. If XYZ and WYV are vertical angles, then XYZ WYV. If mA + mP = 90, then A and P are complementary. If 2 4 and 4 7, then 2 7. If AB + EF = CD and EF=MN, then AB + MN = CD. If CM = MD on CD, then M is the midpoint of CD. If mEFG + mXYZ = 180, then EFG and XYZ are supplementary. If mABC = 90, thenABC is a right angle. If mAPB > 90, then APB is obtuse. ABC ABC. If A and B are right angles, then A B. If 1 2, then m1 = m2. If m1 = m3 and m3 = m2, then m1 = m2. If XY + QP = ST, then XY = ST – QP. If B is between X and Y, then XB + BY= XY. If ABC and XYZ are right angles, then ABC XYZ. If ABC is a right angle, then mABC = 90. If 3(AB)= 3(BC), then AB = BC. If mCXA = 140, then CXA is an obtuse angle. If X is in the interior of JKL such that JKX XKL, then KX is an angle bisector. If 3 and 4 form a linear pair, then m3 + m4 = 180. If 6(x – 10) = 360, then 6x – 60 = 360. If 6x = 360, then x = 60. If 13y – 10 =29, then 13y = 39.