# Geometry Unit 2 Test Logic And Proof Answer Key

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Name__________________________________ Have I Learned This – Geometry Unit 2 Test:
Logic and Proof
Parent Signature_________________________ SOL: G.1
Teacher Signature________________________ Date of Retake___________________
1. In the diagram, 1 2. Which of the following is not true?
a. 3 4
b. m 7 + m 2 + m 4 = 180°
c. m 3 + m 5 = m 4
d. 6 7
e. 4 and 2 are complementary.
Name the property used to make the conclusion.
2. If .
3. If .
Use the diagram to decide whether the statement is true or false.
4. Through points D, B, and E, there exists exactly one plane.
5. Two angles 3 and 5 are each supplementary to 4. If m 5 is 78°, what is m 3?
6. In ABCD, and What is the value of x?
7. Find the length of
True or False:
8. Vertical angles are always supplementary.
9. If two angles are supplements of the same angle, then they must be equal in measure.
10. Identify the property of congruence.
.
Predict the next three numbers.
11. –1, 2, 6, 11, ...
Write the inverse, converse, and contrapositive of the conditional statement.
12. If I ride on the Ferris wheel, then I am not afraid of heights.
Inverse: __________________________
Converse: __________________________
Contrapositive: __________________________
Decide whether the statement is true or false. If false, provide a counterexample.
13. If four points are coplanar, then they are collinear.
Use the diagram and given information to complete the missing reasons in the proof.
14. Given:
Prove:
Rewrite the biconditional statement as two conditional statements.
15. An angle is a right angle if and only if it has a measure of 90°.
Solve the equation and state a reason for each step.
16.
17. Given:
Prove: is supplementary to
18. Write a two-column proof.
Given:
Prove:
Statements: Reasons:
19. Identify the hypothesis and conclusion of the statement.
If today is Friday, then yesterday was Thursday.
20. Given that:
i. Tawana bought a new computer.
ii. All computers depreciate in value.
What conclusion can be logically deduced?
Statements Reasons
1. 1. ?
2. 2. ?
3. 3. ?
4. and are supplementary 4. ?
5. = 180° 5. ?
6. 6. ?
7. = 180° 7. ?
8. is supplementary to 8. ?
Write a two-column proof.
21. Given: , is supplementary to ,
and is supplementary to
Prove:
Statements: Reasons:
22. Decide whether the statement about the diagram is true. Explain your answer using definitions you have learned.
Decide if the argument is valid or invalid. Explain your reasoning.
23. If today is a holiday, then we do not have school.
Today is not a holiday.
Therefore, we do have school.
Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning.
24. The rule in your house is that you must complete all of your homework in order to watch television. You watched
your favorite television show Tuesday night. Therefore, you completed all of your homework on Tuesday.