Name: ________________________ Class: ___________________ Date: __________
Logic, Reasoning, & Proof Item Bank from Geo Test Bank
Multiple Choice
Identify the choice that best completes the statement or answers the question.
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1. Identify the hypothesis and conclusion of this conditional statement:
If tomorrow is Thursday, then yesterday was Tuesday.
a. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was not Tuesday.
b. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is Thursday.
c. Hypothesis: Yesterday was not Tuesday. Conclusion: Tomorrow is Thursday.
d. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.
2. Which statement is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
a. Sara Lucas lives in Springfield.
b. Jonah Lincoln lives in Springfield, Illinois.
c. Billy Jones lives in Chicago, Illinois.
d. Erin Naismith lives in Springfield, Massachusetts.
3. 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.
a. The number is odd.
b. The sum of the digits of the number is divisible by 3.
c. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
d. The number is divisible by 3.
4. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
a. If a point is in the first quadrant, then its coordinates are positive.
b. If a point is not in the first quadrant, then the coordinates of the point are not positive.
c. If the coordinates of a point are positive, then the point is in the first quadrant.
d. If the coordinates of a point are not positive, then the point is not in the first quadrant.
5. Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are congruent, then they have equal measures.
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∠P and ∠Q are congruent.
c. ∠P is the complement of ∠Q.
a. m∠P + m∠Q = 90
d. m∠P ≠ m∠Q
b. m∠P = m∠Q
6. Which statement is the Law of Detachment?
a. If p → q is a true statement and q is true, then p is true.
b. If p → q is a true statement and q is true, then q → p is true.
c. If p → q and q → r are true, then p → r is a true statement.
d. If p → q is a true statement and p is true, then q is true.
7. 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.
a. If a number is a multiple of 64, then it is a multiple of 2.
b. The number is a multiple of 2.
c. The number is a multiple of 8.
d. If a number is not a multiple of 2, then the number is not a multiple of 64.
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ID: A
Name: ________________________
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ID: A
8. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.
If an elephant weighs more than 2,000 pounds, then it weighs more than Jill’s car.
If something weighs more than Jill’s car, then it is too heavy for the bridge.
Smiley the Elephant weighs 2,150 pounds.
a. Smiley is too heavy for the bridge.
b. Smiley weighs more than Jill’s car.
c. If Smiley weighs more than 2000 pounds, then Smiley is too heavy for the bridge.
d. If Smiley weighs more than Jill’s car, then Smiley is too heavy for the bridge.
9. Which statement is the Law of Syllogism?
a. If p → q is a true statement and p is true, then q is true.
b. If p → q is a true statement and q is true, then p is true.
c. if p → q and q → r are true statements, then p → r is a true statement.
d. If p → q and q → r are true statements, then r → p is a true statement.
____ 10. Name the Property of Equality that justifies the statement:
If p = q, then p − r = q − r.
a. Reflexive Property
c. Symmetric Property
b. Multiplication Property
d. Subtraction Property
____ 11. Which statement is an example of the Addition Property of Equality?
a. If p = q then p ⋅ s = q ⋅ s
c. If p = q then p − s = q − s
b. If p = q then p + s = q + s.
d. p = q
____ 12. Name the Property of Congruence that justifies the statement:
If XY ≅ WX , then WX ≅ XY .
a. Symmetric Property
c. Reflexive Property
b. Transitive Property
d. none of these
____ 13. Name the Property of Congruence that justifies the statement:
If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C .
a. Transitive Property
c. Reflexive Property
b. Symmetric Property
d. none of these
Use the given property to complete the statement.
____ 14. Transitive Property of Congruence
If CD ≅ EF and EF ≅ GH, then ______.
a. EF ≅ GH
b. EF ≅ EF
____ 15. Multiplication Property of Equality
If 4x ÷ 2 = 4, then ______.
a. 4 = 4x ⋅ 2
b. 4 = 4x ÷ 2
____ 16. Substitution Property of Equality
If y = 3 and 8x + y = 12, then ______.
a. 8(3) − y = 12
b. 3 − y = 12
c.
d.
CD ≅ GH
CD ≅ EF
c.
d.
4x = 8
4x ⋅ 2 = 8
c.
d.
8x + 3 = 12
8x − 3 = 12
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Name: ________________________
ID: A
Short Answer
17. Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16.
18. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state not
possible. Explain.
Statement 1: If two lines intersect, then they are not parallel.
←⎯
⎯
→
←⎯⎯
→
Statement 2: AB and CD do not intersect.
19. For the given statements below, write the first statement as a conditional in if-then form. Then, if possible, use
the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not
possible. Explain.
A straight angle has a measure of 180.
∠Z is a straight angle.
20. Solve for x. Justify each step.
4x − 9 = 99
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