Geometry Chapter 2 Practice Test

Name: ______________________ Class: _________________ Date: _________ Geo, Chap 2 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. (2-2) Which biconditional is NOT a good definition? a. A whole number is odd if and only if the number is not divisible by 2. b. An angle is straight if and only if its measure is 180. c. A whole number is even if and only if it is divisible by 2. d. A ray is a bisector of an angle if and only if it splits the angle into two angles. Short Answer 2. (2-1) Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular. 3. (2-1) What is the conclusion of the following conditional? A number is divisible by 3 if the sum of the digits of the number is divisible by 3. 4. (2-1) What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. 5. (2-2) For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 3, then x2 = 9. 6. (2-3) Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. I can go to the concert if I can afford to buy a ticket. I can go to the concert. 7. (2-3) If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Statement 1: If x = 3, then 3x – 4 = 5. Statement 2: x = 3 8. (2-3) Use the Law of Syllogism to draw a conclusion from the two given statements. If a number is a multiple of 64,then it is a multiple of 8. If a number is a multiple of 8, then it is a multiple of 2. Fill in each missing reason. 9. (2-4) Given: m∠PQR = x − 5, m∠SQR = x − 11, and m∠PQS = 100. Find x. m∠PQR + m∠SQR = m∠PQS x – 5 + x – 11 = 100 2x – 16 = 100 2x = 116 x = 58 a. _____ b. Substitution Property c. Simplify d. _____ e . Division Property of Equality 10. (2-4) Name the Property of Congruence that justifies the statement: If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C. 11. (2-4) BD bisects ∠ABC. m∠ABC = 7x. m∠ABD = 3x + 25. Find m∠DBC. 12. (2-5) Find the value of x. 13. (2-5) m∠3 = 37. Find m∠1. 14. (2-5) Find the values of x and y. Geo, Chap 2 Practice Test Answer Section MULTIPLE CHOICE 1. ANS: D KEY: biconditional statement SHORT ANSWER 2. ANS: Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular. KEY: conditional statement | hypothesis | conclusion 3. ANS: The number is divisible by 3. KEY: conditional statement | conclusion 4. ANS: If the coordinates of a point are positive, then the point is in the first quadrant. KEY: conditional statement | coverse of a conditional 5. ANS: If x2 = 9, then x = 3. False KEY: conditional statement | coverse of a conditional | biconditional statement 6. ANS: not possible KEY: deductive reasoning | Law of Detachment 7. ANS: 3x – 4 = 5 KEY: Law of Detachment | deductive reasoning 8. ANS: If a number is a multiple of 64, then it is a multiple of 2. KEY: deductive reasoning | Law of Syllogism 9. ANS: Angle Addition Postulate; Addition Property of Equality KEY: Properties of Equality | Angle Addition Postulate | deductive reasoning 10. ANS: KEY: Properties of Congruence Transitive Property 11. ANS: 175 KEY: Properties of Congruence | Properties of Equality | deductive reasoning 12. ANS: KEY: vertical angles | Vertical Angles Theorem 19 13. ANS: 37 KEY: Vertical Angles Theorem | vertical angles 14. ANS: x = 15, y = 17 KEY: Vertical Angles Theorem | vertical angles | supplementary angles | multi-part question