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Geometry - Chapter 2 Earn-A-Try Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Use CAPITAL letters only!! Ex: A,B,C,D; Not a,b,c,d.
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1. Write a conditional statement from the statement.
A horse has 4 legs.
a. If it is a horse then it has 4 legs.
c.
b. It has 4 legs and it is a horse.
d.
Every horse has 4 legs.
If it has 4 legs then it is a horse.
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2. Determine if the conditional statement is true. If false, give a counterexample. If a figure has four sides, then it
is a square.
a. False; A rectangle has four sides, and it is not a square.
b. True.
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3. Write the definition as a biconditional.
An acute angle is an angle whose measure is less than 90°.
a. An angle is acute if and only if its measure is less than 90°.
b. An angle is acute if and only if it is not obtuse.
c. An angle is acute if its measure is less than 90°.
d. An angle’s measure is less than 90° if it is acute.
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4. Write the converse, inverse, and contrapositive of the conditional statement.
If an animal is a bird, then it has two eyes.
a. Converse: If an animal does not have two eyes, then it is not a bird.
Inverse: If an animal is not a bird, then it does not have two eyes.
Contrapositive: If an animal has two eyes, then it is a bird.
b. Converse: All birds have two eyes.
Inverse: All animals have two eyes.
Contrapositive: All birds are animals, and animals have two eyes.
c. Converse: If an animal is not a bird, then it does not have two eyes.
Inverse: If an animal does not have two eyes, then it is not a bird.
Contrapositive: If an animal is a bird, then it has two eyes.
d. Converse: If an animal has two eyes, then it is a bird.
Inverse: If an animal is not a bird, then it does not have two eyes.
Contrapositive: If an animal does not have two eyes, then it is not a bird.
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ID: Z
5. Fill in the blanks to complete the two-column proof.
Given: ∠1 and ∠2 are supplementary. m∠1 = 135°
Prove: m∠2 = 45°
Proof:
Statements
1. ∠1 and ∠2 are supplementary.
2. [1]
3. m∠1 + m∠2 = 180°
4. 135° + m∠2 = 180°
5. m∠2 = 45°
a.
b.
c.
d.
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Reasons
1. Given
2. Given
3. [2]
4. Substitution Property
5. [3]
[1] m∠1 = 135°
[2] Definition of supplementary angles
[3] Subtraction Property of Equality
[1] m∠1 = 135°
[2] Definition of complementary angles
[3] Subtraction Property of Equality
[1] m∠1 = 135°
[2] Definition of supplementary angles
[3] Substitution Property
[1] m∠2 = 135°
[2] Definition of supplementary angles
[3] Subtraction Property of Equality
6. Determine if the conjecture is valid by the Law of Detachment.
Given: If Tommy makes cookies tonight, then Tommy must have an oven. Tommy has an oven.
Conjecture: Tommy made cookies tonight.
a. The conjecture is not valid, because if Tommy didn’t have an oven then he didn’t make
cookies tonight.
b. The conjecture is valid, because Tommy could have an oven but he could make
something besides cookies tonight.
c. The conjecture is not valid, because Tommy could have an oven but he could make
something besides cookies tonight.
d. The conjecture is valid, because if Tommy didn’t have an oven then he didn’t make
cookies tonight
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Name: ________________________
ID: Z
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7. Identify the hypothesis and conclusion of the conditional statement.
If it is raining then it is cloudy.
a. Hypothesis: Rain and clouds happen together.
Conclusion: Rain and clouds do not happen together.
b. Hypothesis: It is raining.
Conclusion: It is cloudy.
c. Hypothesis: Clouds make rain.
Conclusion: Rain does not make clouds.
d. Hypothesis: It is cloudy.
Conclusion: It is raining.
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8. Show that the conjecture is false by finding a counterexample.
a
If a > b , then > 0.
b
c. a = 3, b = 11
a. a = −11, b = 3
b. a = 11, b = 3
d. a = 11, b = −3
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9. Complete the conjecture.
The sum of two odd numbers is ____.
a. even
b. even most of the time
c.
d.
____ 10. Identify the property that justifies the statement.
AB ≅ CD and CD ≅ EF . So AB ≅ EF .
a. Transitive Property of Congruence
c.
b. Substitution Property of Equality
d.
sometimes odd, sometimes even
odd
Symmetric Property of Congruence
Reflexive Property of Congruence
____ 11. 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. Yes, the conjecture is valid.
b. No, the conjecture is not valid.
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____ 12. 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
a2 + b2 = c2.
b. 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
a2 + b2 ≠ c2
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 a right triangle with sides a, b, and c if and only if
a2 + b2 = c2.
d. 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
a2 + b2 = c2.
____ 13. Write a justification for each step.
m∠JKL = 100°
m∠JKL = m∠JKM + m∠MKL
100° = (6x + 8)° + (2x − 4)°
100 = 8x + 4
96 = 8x
12 = x
x = 12
a.
b.
c.
d.
[1]
Substitution Property of Equality
Simplify.
Subtraction Property of Equality
[2]
Symmetric Property of Equality
[1] Angle Addition Postulate
[2] Simplify.
[1] Transitive Property of Equality
[2] Division Property of Equality
[1] Angle Addition Postulate
[2] Division Property of Equality
[1] Segment Addition Postulate
[2] Multiplication Property of Equality
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ID: Z
____ 14. Write a justification for each step, given that EG = FH .
EG = FH
EG = EF + FG
FH = FG + GH
EF + FG = FG + GH
EF = GH
a.
b.
c.
d.
Given information
[1]
Segment Addition Postulate
[2]
Subtraction Property of Equality
[1] Angle Addition Postulate
[2] Subtraction Property of Equality
[1] Segment Addition Postulate
[2] Substitution Property of Equality
[1] Substitution Property of Equality
[2] Transitive Property of Equality
[1] Segment Addition Postulate
[2] Definition of congruent segments
____ 15. What is the truth value of the biconditional formed from the conditional, “If B is the midpoint of A and C, then
AB = BC .” Explain.
a. The conditional is true.
The converse, “If AB = BC then B is the midpoint of AC ” is true.
Since the conditional is true and the converse is true, the biconditional is true.
b. The conditional is false.
The converse, “If AB = BC then B is the midpoint of AC ” is false.
Since the conditional is false and the converse is false, the biconditional is true.
c. The conditional is false.
The converse, “If AB = BC then B is the midpoint of AC ” is true.
Since the conditional is false and the converse is true, the biconditional is false.
d. The conditional is true.
The converse, “If AB = BC then B is the midpoint of AC ” is false.
Since the conditional is true but the converse is false, the biconditional is false.
Numeric Response
16. Find a value for x that provides a counterexample for this conjecture.
4x − 8 4
= .
For all real numbers x,
3x − 6 3
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