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Name: ________________________ Class: ___________________ Date: __________ ID: A Geometry - Chapter 2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Determine if the conjecture is valid by the Law of Syllogism. Given: If you are in California, then you are in the west coast. If you are in Los Angeles, then you are in California. Conjecture: If you are in Los Angeles, then you are in the west coast. a. No, the conjecture is not valid. b. Yes, the conjecture is valid. ____ 2. Use the Law of Syllogism to draw a conclusion from the given information. Given: If two lines are perpendicular, then they form right angles. If two lines meet at a 90° angle, then they are perpendicular. Two lines meet at a 90° angle. a. Conclusion: The lines are parallel. b. Conclusion: The lines are perpendicular and meet at a 90° angle. c. Conclusion: The lines meet at a 90° angle. d. Conclusion: The lines form a right angle. ____ 3. For the conditional statement, write the converse and a biconditional statement. If a figure is a right triangle with sides a, b, and c, then a 2 + b 2 = c 2 . a. Converse: If a figure is not a right triangle with sides a, b, and c, then a 2 + b 2 ≠ c 2 . Biconditional: A figure is a right triangle with sides a, b, and c if and only if a2 + b2 = c2. b. Converse: If a 2 + b 2 = c 2 , then the figure is a right triangle with sides a, b, and c. Biconditional: A figure is a right triangle with sides a, b, and c if and only if a2 + b2 = c2. c. Converse: If a 2 + b 2 ≠ c 2 , then the figure is not a right triangle with sides a, b, and c. Biconditional: A figure is not a right triangle with sides a, b, and c if and only if a2 + b2 ≠ c2 d. Converse: If a 2 + b 2 ≠ c 2 , then the figure is not a right triangle with sides a, b, and c. Biconditional: A figure is a right triangle with sides a, b, and c if and only if a2 + b2 = c2. ____ 4. Determine if the biconditional is true. If false, give a counterexample. A figure is a square if and only if it is a rectangle. a. The biconditional is true. b. The biconditional is false. A rectangle does not necessarily have four congruent sides. c. The biconditional is false. All squares are parallelograms with four 90° angles. d. The biconditional is false. A rectangle does not necessarily have four 90° angles. 1 Name: ________________________ ID: A ____ 5. 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. ____ 6. Solve the equation 4x − 6 = 34. Write a justification for each step. 4x − 6 = 34 Given equation [1] +6 +6 4x = 40 Simplify. 4x 40 = [2] 4 4 x = 10 Simplify. a. b. [1] Substitution Property of Equality; [2] Division Property of Equality [1] Addition Property of Equality; [2] Division Property of Equality c. d. [1] Division Property of Equality; [2] Subtraction Property of Equality [1] Addition Property of Equality; [2] Reflexive Property of Equality Short Answer 7. Find the next item in the pattern 2, 3, 5, 7, 11, ... 8. How many true conditional statements may be written using the following statements? n is a rational number. n is an integer. n is a whole number. 9. Write the conditional statement and converse within the biconditional. A rectangle is a square if and only if all four sides of the rectangle have equal lengths. 10. Identify the property that justifies the statement. AB ≅ CD and CD ≅ EF . So AB ≅ EF . 2 Name: ________________________ ID: A Matching Match each vocabulary term with its definition. a. conjecture b. inductive reasoning c. deductive reasoning d. conclusion e. biconditional statement f. hypothesis g. counterexample h. conditional statement ____ 11. an example that proves that a conjecture or statement is false ____ 12. a statement that is believed to be true ____ 13. the part of a conditional statement following the word then ____ 14. the part of a conditional statement following the word if ____ 15. the process of reasoning that a rule or statement is true because specific cases are true ____ 16. a statement that can be written in the form “if p, then q,” where p is the hypothesis and q is the conclusion Match each vocabulary term with its definition. a. conclusion b. converse c. inverse d. negation e. hypothesis f. truth value g. contrapositive ____ 17. for a statement, either true (T) or false (F) ____ 18. operations that undo each other ____ 19. the contradiction of a statement by using “not,” written as ∼ ____ 20. the statement formed by exchanging the hypothesis and conclusion of a conditional statement ____ 21. the statement formed by both exchanging and negating the hypothesis and conclusion 1 Name: ________________________ ID: A Match each vocabulary term with its definition. a. logically equivalent statements b. deductive reasoning c. biconditional statement d. inductive reasoning e. polygon f. quadrilateral g. pentagon h. definition i. triangle ____ 22. a statement that describes a mathematical object and can be written as a true biconditional statement ____ 23. statements that have the same truth value ____ 24. a four-sided polygon ____ 25. 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 ____ 26. the process of using logic to draw conclusions ____ 27. a statement that can be written in the form “p if and only if q” ____ 28. a three-sided polygon Match each vocabulary term with its definition. a. deductive reasoning b. paragraph proof c. proof d. theorem e. inductive reasoning f. two-column proof g. flowchart proof ____ 29. 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 ____ 30. a statement that has been proven ____ 31. a style of proof in which the statements and reasons are presented in paragraph form ____ 32. an argument that uses logic to show that a conclusion is true ____ 33. a style of proof that uses boxes and arrows to show the structure of the proof 4 ID: A Geometry - Chapter 2 Review Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. ANS: ANS: ANS: ANS: ANS: ANS: B D B B B B TOP: TOP: TOP: TOP: TOP: TOP: 2-3 Using Deductive Reasoning to Verify Conjectures 2-3 Using Deductive Reasoning to Verify Conjectures 2-4 Biconditional Statements and Definitions 2-4 Biconditional Statements and Definitions 2-4 Biconditional Statements and Definitions 2-5 Algebraic Proof SHORT ANSWER 7. ANS: 13 TOP: 2-1 Using Inductive Reasoning to Make Conjectures 8. ANS: 3 conditional statements TOP: 2-2 Conditional Statements 9. ANS: Conditional: If all four sides of the rectangle have equal lengths, then it is a square. Converse: If a rectangle is a square, then its four sides have equal lengths. TOP: 2-4 Biconditional Statements and Definitions 10. ANS: Transitive Property of Congruence TOP: 2-5 Algebraic Proof MATCHING 11. 12. 13. 14. 15. 16. ANS: ANS: ANS: ANS: ANS: ANS: G A D F B H TOP: TOP: TOP: TOP: TOP: TOP: 2-1 Using Inductive Reasoning to Make Conjectures 2-1 Using Inductive Reasoning to Make Conjectures 2-2 Conditional Statements 2-2 Conditional Statements 2-1 Using Inductive Reasoning to Make Conjectures 2-2 Conditional Statements 17. 18. 19. 20. ANS: ANS: ANS: ANS: F C D B TOP: TOP: TOP: TOP: 2-2 Conditional Statements 2-2 Conditional Statements 2-2 Conditional Statements 2-2 Conditional Statements 1 ID: A 21. ANS: G TOP: 2-2 Conditional Statements 22. 23. 24. 25. 26. 27. 28. ANS: ANS: ANS: ANS: ANS: ANS: ANS: H A F E B C I TOP: TOP: TOP: TOP: TOP: TOP: TOP: 2-4 Biconditional Statements and Definitions 2-2 Conditional Statements 2-4 Biconditional Statements and Definitions 2-4 Biconditional Statements and Definitions 2-3 Using Deductive Reasoning to Verify Conjectures 2-4 Biconditional Statements and Definitions 2-4 Biconditional Statements and Definitions 29. 30. 31. 32. 33. ANS: ANS: ANS: ANS: ANS: F D B C G TOP: TOP: TOP: TOP: TOP: 2-6 Geometric Proof 2-6 Geometric Proof 2-7 Flowchart and Paragraph Proofs 2-5 Algebraic Proof 2-7 Flowchart and Paragraph Proofs 2