Name: Class: Date: Geometry - Chapter 2 Corrective 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Make a table of values for the rule x 2 16x + 64 when x is an integer from 1 to 6. Make a conjecture about the type of number generated by the rule. Continue your table. What value of x generates a counterexample? a. The pattern appears to be an decreasing set of perfect squares. x = 9 generates a counterexample. b. The pattern appears to be a decreasing set of prime numbers. x = 8 generates a counterexample. c. The pattern appears to be a decreasing set of perfect squares. x = 7 generates a counterexample. d. The pattern appears to be an increasing set of perfect squares. x = 8 generates a counterexample. 2. Write the definition as a biconditional. An acute angle is an angle whose measure is less than 90. a. An angle is acute if its measure is less than 90. b. An angle is acute if and only if its measure is less than 90. c. An angle s measure is less than 90 if it is acute. d. An angle is acute if and only if it is not obtuse. 3. Write a justification for each step. m JKL = 100 m JKL = m JKM + m MKL [1] 100 = (6x + 8) + (2x 4) Substitution Property of Equality 100 = 8x + 4 Simplify. 96 = 8x Subtraction Property of Equality 12 = x [2] x = 12 Symmetric Property of Equality a. [1] Transitive Property of Equality [2] Division Property of Equality b. [1] Angle Addition Postulate [2] Division Property of Equality c. [1] Angle Addition Postulate [2] Simplify. d. [1] Segment Addition Postulate [2] Multiplication Property of Equality 1
Name: 4. There is a myth that a duck s quack does not echo. A group of scientists observed a duck in a special room, and they found that the quack does echo. Therefore, the myth is false. Is the conclusion a result of inductive or deductive reasoning? a. Since the conclusion is based on a pattern of observation, it is a result of inductive reasoning. b. Since the conclusion is based on a pattern of observation, it is a result of deductive reasoning. c. Since the conclusion is based on logical reasoning from scientific research, it is a result of inductive reasoning. d. Since the conclusion is based on logical reasoning from scientific research, it is a result of deductive reasoning. 5. Fill in the blanks to complete the two-column proof. Given: 1 and 2 are supplementary. m 1 = 135 Prove: m 2 = 45 Proof: Statements Reasons 1. 1 and 2 are supplementary. 1. Given 2. [1] 2. Given 3. m 1 + m 2 = 180 3. [2] 4. 135 + m 2 = 180 4. Substitution Property 5. m 2 = 45 5. [3] a. [1] m 2 = 135 [2] Definition of supplementary angles [3] Subtraction Property of Equality b. [1] m 1 = 135 [2] Definition of supplementary angles [3] Substitution Property c. [1] m 1 = 135 [2] Definition of supplementary angles [3] Subtraction Property of Equality d. [1] m 1 = 135 [2] Definition of complementary angles [3] Subtraction Property of Equality 2
Name: Matching a. conjecture b. inductive reasoning c. deductive reasoning d. conclusion e. biconditional statement f. hypothesis g. counterexample h. conditional statement 6. the part of a conditional statement following the word if 7. the part of a conditional statement following the word then 8. the process of reasoning that a rule or statement is true because specific cases are true 9. a statement that can be written in the form if p, then q, where p is the hypothesis and q is the conclusion 10. an example that proves that a conjecture or statement is false 11. a statement that is believed to be true a. logically equivalent statements b. deductive reasoning c. biconditional statement d. inductive reasoning e. polygon f. quadrilateral g. pentagon h. definition i. triangle 12. a three-sided polygon 13. a closed plane figure formed by three or more segments such that each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear 14. a statement that describes a mathematical object and can be written as a true biconditional statement 15. a four-sided polygon 16. a statement that can be written in the form p if and only if q 17. the process of using logic to draw conclusions 18. statements that have the same truth value 1
Name: a. conclusion b. converse c. inverse d. negation e. hypothesis f. truth value g. contrapositive 19. the statement formed by both exchanging and negating the hypothesis and conclusion 20. the contradiction of a statement by using not, written as 21. the statement formed by exchanging the hypothesis and conclusion of a conditional statement 22. operations that undo each other 23. for a statement, either true (T) or false (F) a. deductive reasoning b. paragraph proof c. proof d. theorem e. inductive reasoning f. two-column proof g. flowchart proof 24. a style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column 25. a style of proof that uses boxes and arrows to show the structure of the proof 26. a style of proof in which the statements and reasons are presented in paragraph form 27. a statement that has been proven 28. an argument that uses logic to show that a conclusion is true 4
Name: Short Answer 29. Write a justification for each step, given that EG = FH. EG = FH Given information EG = EF + FG [1] FH = FG + GH Segment Addition Postulate EF + FG = FG + GH [2] EF = GH Subtraction Property of Equality 30. Write a conditional statement from the statement. A horse has 4 legs. 5
Geometry - Chapter 2 Corrective 1 Answer Section MULTIPLE CHOICE 1. ANS: A TOP: 2-1 Using Inductive Reasoning to Make Conjectures 2. ANS: B TOP: 2-4 Biconditional Statements and Definitions 3. ANS: B TOP: 2-5 Algebraic Proof 4. ANS: A TOP: 2-3 Using Deductive Reasoning to Verify Conjectures 5. ANS: C TOP: 2-6 Geometric Proof MATCHING 6. ANS: F TOP: 2-2 Conditional Statements 7. ANS: D TOP: 2-2 Conditional Statements 8. ANS: B TOP: 2-1 Using Inductive Reasoning to Make Conjectures 9. ANS: H TOP: 2-2 Conditional Statements 10. ANS: G TOP: 2-1 Using Inductive Reasoning to Make Conjectures 11. ANS: A TOP: 2-1 Using Inductive Reasoning to Make Conjectures 12. ANS: I TOP: 2-4 Biconditional Statements and Definitions 13. ANS: E TOP: 2-4 Biconditional Statements and Definitions 14. ANS: H TOP: 2-4 Biconditional Statements and Definitions 15. ANS: F TOP: 2-4 Biconditional Statements and Definitions 16. ANS: C TOP: 2-4 Biconditional Statements and Definitions 17. ANS: B TOP: 2-3 Using Deductive Reasoning to Verify Conjectures 18. ANS: A TOP: 2-2 Conditional Statements 19. ANS: G TOP: 2-2 Conditional Statements 20. ANS: D TOP: 2-2 Conditional Statements 21. ANS: B TOP: 2-2 Conditional Statements 22. ANS: C TOP: 2-2 Conditional Statements 23. ANS: F TOP: 2-2 Conditional Statements 24. ANS: F TOP: 2-6 Geometric Proof 25. ANS: G TOP: 2-7 Flowchart and Paragraph Proofs 26. ANS: B TOP: 2-7 Flowchart and Paragraph Proofs 27. ANS: D TOP: 2-6 Geometric Proof 28. ANS: C TOP: 2-5 Algebraic Proof 1
SHORT ANSWER 29. ANS: [1] Segment Addition Postulate [2] Substitution Property of Equality TOP: 2-6 Geometric Proof 30. ANS: If it is a horse then it has 4 legs. TOP: 2-2 Conditional Statements 2