Name: Class: Date: ID: A Chapter 2 Practice Test 1. What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 4 is also divisible by 8. 2. What is the conclusion of the following conditional? A number is divisible by 2 if the number is even. 3. Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular. 4. Write this statement as a conditional in if-then form: All triangles have three sides. 5. What is the converse of the following conditional? If a point is in the fourth quadrant, then its coordinates are negative. 6. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 7, then x 2 = 49. 7. Is the following definition of dog reversible? If yes, write it as a true biconditional. A dog is a mammal. 1
Name: ID: A 8. What is the value of x? Identify the missing justifications. m PQR = x 5, m SQR = x 7, and m PQS =100. m PQR +m SQR = m PQS x 5 + x 7 = 100 2x 12 = 100 2x = 112 x = 56 a. b. Substitution Property c. Simplify d. e. Division Property of Equality 9. BD bisects ABC. m ABC = 7x. m ABD = 3x+36. Find m DBC. 10. Name the Property of Equality that justifies this statement: If l = m, then m=l. Use the given property to complete the statement. 11. Transitive Property of Congruence If CD EFandEF GH,then. 12. Multiplication Property of Equality If 5x 9=36, then. 13. Substitution Property of Equality If y= 5and7x+y=11, then. 2
Name: ID: A 14. Name the Property of Congruence that justifies the statement: If MN LK,thenLK MN. 15. Name the Property of Congruence that justifies this statement: If A Band B C, then A C. 16. Complete the two-column proof. Given: 12x 6y=5;x= 5 Prove: 65 6 =y 12x 6y=5;x= 5 60 6y=5 6y=65 y= 65 6 65 6 a. b. c. d. =y e. 17. Complete the two-column proof. Given: x 5 +9=11 Prove: x=10 x +9=11 a. 5 x 5 =2 b. x=10 c. 3
Name: ID: A 18. What is the value of x? 19. What is the value of x? 20. Find the values of x and y. 4
ID: A Chapter 2 Practice Test Answer Section 1. ANS: 12 PTS: 1 DIF: L2 REF: 2-1 Patterns and Inductive Reasoning OBJ: 2-1.1 To use inductive reasoning to make conjectures NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.a TOP: 2-1 Problem 5 Finding a Counterexample KEY: conjecture counterexample 2. ANS: The number is divisible by 2. PTS: 1 DIF: L3 REF: 2-2 Conditional Statements OBJ: 2-2.1 To recognize conditional statements and their parts NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.a TOP: 2-2 Problem 1 Identifying the Hypothesis and the Conclusion KEY: conditional statement conclusion 3. ANS: Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular. PTS: 1 DIF: L3 REF: 2-2 Conditional Statements OBJ: 2-2.1 To recognize conditional statements and their parts NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.a TOP: 2-2 Problem 1 Identifying the Hypothesis and the Conclusion KEY: conditional statement hypothesis conclusion 4. ANS: If a figure is a triangle, then it has three sides. PTS: 1 DIF: L2 REF: 2-2 Conditional Statements OBJ: 2-2.1 To recognize conditional statements and their parts NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.a TOP: 2-2 Problem 2 Writing a Conditional KEY: hypothesis conclusion conditional statement 5. ANS: If the coordinates of a point are negative, then the point is in the fourth quadrant. PTS: 1 DIF: L2 REF: 2-2 Conditional Statements OBJ: 2-2.2 To write converses, inverses, and contrapositives of conditionals NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 TOP: 2-2 Problem 4 Writing and Finding Truth Values of Statements KEY: conditional statement converse of a conditional 1
ID: A 6. ANS: If x 2 = 49, then x = 7. False PTS: 1 DIF: L3 REF: 2-3 Biconditionals and Definitions OBJ: 2-3.1 To write biconditionals and recognize good definitions NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.1.c TOP: 2-3 Problem 1 Writing a Biconditional KEY: conditional statement converse of a conditional biconditional statement 7. ANS: The reverse is false. PTS: 1 DIF: L3 REF: 2-3 Biconditionals and Definitions OBJ: 2-3.1 To write biconditionals and recognize good definitions NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.1.c TOP: 2-3 Problem 3 Writing a Definition as a Biconditional KEY: biconditional statement 8. ANS: Angle Addition Postulate; Addition Property of Equality TOP: 2-5 Problem 1 Justifying Steps When Solving an Equation KEY: Properties of Equality Angle Addition Postulate deductive reasoning 9. ANS: 252 PTS: 1 DIF: L4 REF: 2-5 Reasoning in Algebra and Geometry TOP: 2-5 Problem 1 Justifying Steps When Solving an Equation KEY: Properties of Congruence Properties of Equality deductive reasoning 10. ANS: Symmetric Property PTS: 1 DIF: L2 REF: 2-5 Reasoning in Algebra and Geometry KEY: Properties of Equality Symmetric Property 11. ANS: CD GH KEY: Properties of Congruence Transitive Property 2
ID: A 12. ANS: 5x=324 KEY: Properties of Equality 13. ANS: 7x 5=11 KEY: Properties of Equality 14. ANS: Symmetric Property PTS: 1 DIF: L2 REF: 2-5 Reasoning in Algebra and Geometry KEY: Properties of Congruence Symmetric Property 15. ANS: Transitive Property PTS: 1 DIF: L2 REF: 2-5 Reasoning in Algebra and Geometry KEY: Properties of Congruence Transitive Property 16. ANS: a. Given b. Substitution Property c. Addition Property of Equality d. Division Property of Equality e. Symmetric Property of Equality TOP: 2-5 Problem 3 Writing a Two-Column Proof KEY: Properties of Equality Proof Two-column Proof 3
ID: A 17. ANS: a. Given b. Subtraction Property of Equality c. Multiplication Property of Equality PTS: 1 DIF: L2 REF: 2-5 Reasoning in Algebra and Geometry TOP: 2-5 Problem 3 Writing a Two-Column Proof KEY: Properties of Equality proof Two-column Proof 18. ANS: 16 PTS: 1 DIF: L3 REF: 2-6 Proving Angles Congruent OBJ: 2-6.1 To prove and apply theorems about angles NAT: CC G.CO.9 G.5.b TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: vertical angles Vertical Angles Theorem 19. ANS: 60 PTS: 1 DIF: L2 REF: 2-6 Proving Angles Congruent OBJ: 2-6.1 To prove and apply theorems about angles NAT: CC G.CO.9 G.5.b TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: vertical angles Vertical Angles Theorem 20. ANS: x = 15, y = 17 PTS: 1 DIF: L4 REF: 2-6 Proving Angles Congruent OBJ: 2-6.1 To prove and apply theorems about angles NAT: CC G.CO.9 G.5.b TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: Vertical Angles Theorem vertical angles supplementary angles multi-part question 4