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Logic and Proof

Total questions: 42

Worksheet time: 54mins

Name
Class
Date
1.

If something is an angle, then it is acute. What is an appropriate counter-example?

a)

70⁰

b)

45⁰

c)

120⁰

d)

True. There is no counterexample.

2.
Use inductive reasoning to finish the pattern: 400, 200, 100, 50, ____
a)
-150
b)
25
c)
12.5
d)
0
3.

A conjecture is:

a)

a false example in a compound statement

b)

a compound statement using and or nor

c)

a concluding statement reached during inductive reasoning

d)

an educated guess based on empirical data, collected by a calculator

4.

Inductive Reasoning means...

a)

Guessing

b)

Testing and observing patterns to make conjectures

c)

Explaining why

d)

Adding numbers together

5.
Given, "If I have a Siberian Husky, then I have a dog." Identify the hypothesis.
a)
If I have a Siberian Husky.
b)
I have a Siberian Husky.
c)
Then I have a dog.
d)
I have a dog.
6.
Given, "If I have a Siberian Husky, then I have a dog." Identify the conclusion.
a)
If I have a Siberian Husky.
b)
I have a Siberian Husky.
c)
Then I have a dog.
d)
I have a dog.
7.
Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.
a)
If the measures of the angles are equal, then the angles are congruent.
b)
"If angles are not congruent, then the measures of the angles are not equal."
c)
If the measures of the angles are not equal, then the angles are not congruent.
d)
If the angles are not congruent, then the measure of the angles are equal.
8.
Use the law of syllogism to draw a conclusion from the two given statements:
Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy
a)
You have more energy
b)
If you exercise regularly, then you have more energy
c)
You have a healthy body
d)
If you do not have a healthy body, then you do not exercise regularly
9.

If Bill wears a green shirt, then he will pass the test. Bill wore a green shirt.


What can you conclude?

a)

Bill wore a green shirt.

b)

Bill passed the test.

c)

Nothing

10.
Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
Statement 1: If I study for one hour each day, then I will score well on the exam
Statement 2: I will score well on the exam
a)
 I study for 1 hour each day.
b)
I do not study for 1 hour each day
c)
If I do well on the exam, I studied for 1 hour each day.
d)
not possible
11.

Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.

a)

Inductive

b)

Deductive

12.

Reasoning based on specific examples and patterns used to form conjectures is called ______________ reasoning.

a)

Inductive

b)

Deductive

13.

Which of the following theorems/postulates would verify that ∠COB & ∠AOD are congruent?

a)

Straight Angle Theorem

b)

Congruent Compliments Theorem

c)

Vertical Angles Theorem

d)

Linear Pair Theorem

14.

Which of the following statements is the inverse of

"If you do not understand geometry, then you do not know how to reason deductively."?

a)

If you reason deductively, then you understand geometry.

b)

If you understand geometry, then you reason deductively.

c)

If the do not reason deductively, then you understand geometry.

d)

If you understand geometry, then you do not know how to reason deductively.

15.

Which of the following statements is the contrapositive of

"If you understand logic, you will be a good consumer."?

a)

If you are a good consumer, then you understand logic.

b)

If you are not a good consumer, then you do not understand logic.

c)

If you do not understand logic, then you will not be a good consumer.

d)

If you understand logic, you will not be a good consumer.

16.

Deductive reasoning is the type of reasoning used when people make conjectures.

a)

True

b)

False

17.

Choose reason 2, 3 and 4. (In order)

Hint: Complete the entire table first !

a)

Reflexive property, Subtraction property and addition property.

b)

Subtraction property, substitution and reflexive property

c)

Subtraction property, addition property and division property

d)

Reflective property, addition property and division property

18.

If two angles form a linear pair, what can you conclude about the angles?

a)

The two angles are congruent.

b)

The two angles are complementary.

c)

The two angles are supplementary.

d)

The two angles are right angles.

19.

Fill in the blank to give a reason for the statement below. You may refer to the Properties of Equality shown.

If m∠1=m∠2 and m∠2=m∠3, then m∠1=m∠3

by the__________ property of equality.

a)

addition

b)

subtraction

c)

symmetric

d)

transitive

e)

multiplication

20.

What is this? ¿Que es esto?

a)

Conditional statement Enunciado condicional

b)

Inverse Inversa

c)

Converse Conversa

d)

THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS! ESTA ES UNA CLASE DE GEOMETRIA !!! ¡DAME NÚMEROS!

21.

What is q → p? ¿Qué es q → p?

a)

conditional enunciado

b)

converse conversa

c)

inverse inversa

d)

contrapositive contrapositiva

22.

What is ~p → ~q? ¿Qué es ~ p → ~ q?

a)

conditional enunciado

b)

converse conversa

c)

inverse inversa

d)

contrapositive contrapositiva

23.

What is ~q → ~p? ¿Qué es ~ q → ~ p?

a)

conditional enunciado

b)

converse conversa

c)

inverse inversa

d)

contrapositive contrapositiva

24.

Which of the following is used to prove that a conjecture is false? ¿Cuál de las siguientes opciones se usa para probar que una conjetura es falsa?

a)

Counterexample Contraejemplo

b)

Inductive Reasoning Razonamiento inductivo

c)

Concluding statement Declaración final

d)

Conjecture Conjetura

25.
What can be assumed? 
C is the midpoint of segment AB
a)
AB = BC
b)
AC=CB
c)
Nothing
d)
BA=CA
26.
Name the property:
 2(x + 3) = 2x + 6
a)
Division
b)
Distributive
c)
Reflexive
d)
Substitution
27.
Name the property described:
If PQ = RS then RS = PQ
a)
Reflexive
b)
Symmetric
c)
Transitive
d)
Addition
28.
What is always the reason for the first statement in a proof?
a)
Given
b)
Handed
c)
Donated
d)
Stated
29.
What is the reason?
a)
Definition of equal
b)
Definition of Angle
c)
Angle Addition
d)
Definition of congruence
30.
What is the reason?
a)
Definition of Complementary
b)
Definition of 180 
c)
Definition of supplementary
d)
Angle Addition
31.

Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.

a)

If the measures of the angles are equal, then the angles are congruent.

b)

"If angles are not congruent, then the measures of the angles are not equal."

c)

If the measures of the angles are not equal, then the angles are not congruent.

d)

If the angles are not congruent, then the measure of the angles are equal.

32.
What is the REASON for Statement #2?
a)
Given
b)
Definition of Complementary Angles
c)
Substitution Property
d)
Reflexive Property of Congruence
33.
What is the REASON for Statement #3?
a)
Given
b)
Definition of Complementary Angles
c)
Substitution Property
d)
Reflexive Property of Congruence
34.
What is the REASON for Statement #4?
a)
Substitution Property
b)
Distributive Property
c)
Transitive Property
d)
Combine Like Terms
35.
What is the REASON for Statement #5?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
36.
What is the REASON for Statement #6?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
37.
What is the justification (reason)?
a)
reflexive property
b)
definition of segment bisect
c)
definition of a midpoint
d)
substitution property
38.
If <1 and <2 are complementary, then m<1 + m<2 = 90
a)
Addition POE
b)
Subtraction POE
c)
Def of right angle
d)
Def of Complementary Angles
39.
What is the justification?
a)
Symmetric Prop.
b)
Angle addition postulate
c)
Reflexive Prop
d)
Transitive Prop.
40.
a)
addition POE
b)
angle addition POE
c)
subtraction POE
d)
substitution POE
41.
If A = B, then 8A = 8B
a)
Multiplication POE
b)
Division POE
c)
Reflexive POE
d)
Addition POE
42.
What is the missing statement in the proof?
a)
Addition p.o.e
b)
Segment Addition Postulate
c)
Substitution p.o.e
d)
Transitive p.o.e