Geometry - Chapter 2 Review

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1 Name: Class: Date: 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 a 2 + b 2 = c 2. 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 a 2 + b 2 = c 2. 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 a 2 + b 2 c 2 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 a 2 + b 2 = c 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

2 Name: 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] 4x = 40 Simplify. 4x = [2] x = 10 Simplify. a. [1] Substitution Property of Equality; [2] Division Property of Equality b. [1] Addition Property of Equality; [2] Division Property of Equality c. [1] Division Property of Equality; [2] Subtraction Property of Equality d. [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, 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

3 Name: Matching 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 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

4 Name: 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 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

5 Geometry - Chapter 2 Review Answer Section MULTIPLE CHOICE 1. ANS: B TOP: 2-3 Using Deductive Reasoning to Verify Conjectures 2. ANS: D TOP: 2-3 Using Deductive Reasoning to Verify Conjectures 3. ANS: B TOP: 2-4 Biconditional Statements and Definitions 4. ANS: B TOP: 2-4 Biconditional Statements and Definitions 5. ANS: B TOP: 2-4 Biconditional Statements and Definitions 6. ANS: B TOP: 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. ANS: G TOP: 2-1 Using Inductive Reasoning to Make Conjectures 12. ANS: A TOP: 2-1 Using Inductive Reasoning to Make Conjectures 13. ANS: D TOP: 2-2 Conditional Statements 14. ANS: F TOP: 2-2 Conditional Statements 15. ANS: B TOP: 2-1 Using Inductive Reasoning to Make Conjectures 16. ANS: H TOP: 2-2 Conditional Statements 17. ANS: F TOP: 2-2 Conditional Statements 18. ANS: C TOP: 2-2 Conditional Statements 19. ANS: D TOP: 2-2 Conditional Statements 20. ANS: B TOP: 2-2 Conditional Statements 1

6 21. ANS: G TOP: 2-2 Conditional Statements 22. ANS: H TOP: 2-4 Biconditional Statements and Definitions 23. ANS: A TOP: 2-2 Conditional Statements 24. ANS: F TOP: 2-4 Biconditional Statements and Definitions 25. ANS: E TOP: 2-4 Biconditional Statements and Definitions 26. ANS: B TOP: 2-3 Using Deductive Reasoning to Verify Conjectures 27. ANS: C TOP: 2-4 Biconditional Statements and Definitions 28. ANS: I TOP: 2-4 Biconditional Statements and Definitions 29. ANS: F TOP: 2-6 Geometric Proof 30. ANS: D TOP: 2-6 Geometric Proof 31. ANS: B TOP: 2-7 Flowchart and Paragraph Proofs 32. ANS: C TOP: 2-5 Algebraic Proof 33. ANS: G TOP: 2-7 Flowchart and Paragraph Proofs 2