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WorksheetsUnit 2: Logic and Proof
Total questions: 46
Worksheet time: 57mins
Name
Class
Date
1.
Which number is a counterexample to the following statement? :
All numbers that are divisible by 2 are divisible by 4
All numbers that are divisible by 2 are divisible by 4
a)
0
b)
12
c)
28
d)
42
2.
a)
A
b)
B
c)
C
d)
D
3.
Used to prove that a conjecture is false.
a)
Counterexample
b)
Inductive Reasoning
c)
Concluding statement
d)
Conjecture
4.
Complete the conjecture. Think of examples to help.
The product of any two odd numbers is _____________
The product of any two odd numbers is _____________
a)
even
b)
odd
c)
zero
d)
positive
5.
Complete the conjecture. Think of examples to help.
The sum of an odd number and an even number is ________________
The sum of an odd number and an even number is ________________
a)
even
b)
odd
c)
zero
d)
positive
6.
Which is a counterexample of: If a four sided shape has two sides the same length, then it must be a rectangle.
a)
quadrilateral
b)
rectangle
c)
square
d)
triangle
7.
The type of reasoning where a person makes conclusions based on observations and patterns is called...
a)
Inductive reasoning
b)
Deductive reasoning
c)
Conjecture
d)
Experiments
8.
What are the missing numbers in this pattern?
23, 33, ___, 53, ___, 73
23, 33, ___, 53, ___, 73
a)
32, 62
b)
42, 63
c)
43, 63
d)
42, 62
9.
Complete the conjecture. Think of examples to help.
The difference of any two odd numbers is _______
The difference of any two odd numbers is _______
a)
even
b)
odd
c)
zero
d)
positive
10.
Which is a counterexample of: The difference of two numbers is less than the greater number.
a)
(5) - (2) = 3
b)
(-5) - (4) = -9
c)
(2) - 0 = 2
d)
(3) - (3) = 0
11.
Use inductive reasoning to predict the next three numbers in the pattern. 9, 3, 1, 1/3, 1/9
a)
1/27, 1/81, 1/243
b)
1, 2, 3
c)
27, 81, 243
d)
6, 12, 15
12.
What is multiplication property of equality
a)
a. If a=b, then a+c=b+c
b)
b. If a=b, then a-c=b-c
c)
c. If a=b, then ac=bc
d)
d. If a=b, then a/c=b/c
13.
Identify the property of equality used & the solution.
a)
division: 7
b)
addition: - 40
c)
multiplication: - 30
d)
division: - 7
14.
Identify the property of equality used & the solution.
a)
division: 50
b)
multiplication: 50
c)
multiplication: -50
d)
addition: -5
15.
Step 2 is what
a)
Substitution property (simplify)
b)
Multiplication property of equality
c)
Division property of equality
d)
Distributive Property
16.
What is step 3
a)
Addition property of equality
b)
Substitution property (simplify)
c)
Subtraction property of equality
17.
What is step 5
a)
Substitution property (simplify)
b)
Addition property of equality
c)
Division property of equality
18.
What is step 4
a)
Substitution property (simplify)
b)
Addition property of equality
c)
Subtraction property of equality
19.
What is step 6
a)
Subtraction property of equality
b)
Addition property of equality
c)
Division property of equality
20.
3(w + 4) = 3w + 12 is an example of...
a)
Inverse Property
b)
Distributive Property
c)
Multiplicative Inverse
d)
Associative Property
21.
What is the Symmetric property?
a)
If a=b, then a can be substituted for b in any equation or expression
b)
a(b+c)=ab+ac
c)
For any real number a, a=a .
d)
If a=b, then b=a
22.
What is the justification?
a)
Symmetric Prop.
b)
Angle addition postulate
c)
Reflexive Prop
d)
Transitive Prop.
23.
What is the justification that the measure of angle DAE plus the measure of angle EAF = 90 degrees?
a)
definition of supplementary angles
b)
definition of complementary angles
c)
Vertical Angles Theorem
d)
definition of bisect
24.
What is the justification?
a)
Transitive Property
b)
Substitution Property
c)
Reflexive Property
d)
Symmetric Property
25.
What allows to say that angle IKH is congruent to angle GKJ?
a)
definition of vertical angles
b)
Linear Pairs Theorem
c)
definition of a straight angle
d)
Vertical angles theorem
26.
What is the justification?
a)
reflexive property
b)
definition of bisect
c)
definition of a midpoint
d)
substitution property
27.
What is the justification?
a)
Reflexive Prop.
b)
Symmetric Prop.
c)
Transitive Prop.
d)
Substitution
28.
What is the justification that segment GI is congruent to segment IH?
a)
segment addition postulate
b)
definition of perpendicular
c)
definition of midpoint
d)
definition of a segment
29.
What would allow you to write this equation?
a)
definition of complementary angles
b)
definition of supplementary angles
c)
Transitive Property
d)
Symmetric Property
30.
If we are given that angles C and D are complementary angles what can we conclude?
a)
C + D = 180 by definition of right angles
b)
C + D = 90 by definition of complementary angles
c)
C + D = 180 by definition of complentary angles
d)
C and D are congruent angles
31.
When starting a proof you always start with:
a)
Given information
b)
What it wants you to prove
c)
Equal Angles
d)
Linear Angles
32.
What is the reason for the above?
a)
Angle Addition Postulate
b)
Segment Addition Postulate
c)
Definition of Midpoint
d)
Transitive Property of Congruence
33.
What is the reasoning behind the following?
Given: ∠1 and ∠2 are supplementary. ∠2 and ∠3 are supplementary.
Prove: ∠1 ≅ ∠3
Given: ∠1 and ∠2 are supplementary. ∠2 and ∠3 are supplementary.
Prove: ∠1 ≅ ∠3
a)
Congruent Supplements Theorem
b)
Reflexive Property of Congruence
c)
Definition of Supplementary Angles
d)
Definition of Congruence
34.
What is the reason for the statements below?
Given: m∠1 + m∠2 = 90
Prove: ∠1 and ∠2 are complementary.
Given: m∠1 + m∠2 = 90
Prove: ∠1 and ∠2 are complementary.
a)
Definition of Complementary Angles
b)
Congruent Complements Theorem
c)
Definition of Right Angles
d)
Angle Addition Postulate
35.
What is the reason for the statement below?
Given: m∠1 = 63
m∠1 + m∠2 = 90
Prove: 63 + m∠2 = 90
Given: m∠1 = 63
m∠1 + m∠2 = 90
Prove: 63 + m∠2 = 90
a)
Reflexive Property of Equality
b)
Symmetric Property of Equality
c)
Transitive Property of Equality
d)
Substitution Property of Equality
36.
Which best fills in the blank on Statement 3 ?
a)
RS + RS = RT
b)
ST + ST = RT
c)
RS + ST = RT
d)
RS = ST
37.
Fill in the statement for number 4.
a)
RA=RE +AE
b)
EL = EA + AL
c)
RE +EA= EA +AL
d)
RA = EL
38.
Fill in the reason for 5.
a)
Addition Postulate
b)
Substitution property
c)
Definition of midpoint
d)
Segment Addition Postulate
39.
Which of the following below would fill in the Reasons in the proper order?
a)
Given; Definition of bisect; Transitive; Given, Definition of bisect
b)
Given; Transitive; Given; Definition of bisect; Definition of bisect
c)
Given; Definition of bisect; Given; Definition of bisect; Transitive
40.
What is the correct reason for
Reason #3?
a)
Definition of a Straight Angle
b)
Prove
c)
Definition of a Supplementary Angles
d)
Transitive Property
41.
What is the answer to #4?
a)
Prove
b)
Multiplication Property
c)
Division Property
d)
Addition Property
42.
What is the REASON for Statement #2?
a)
Given
b)
Definition of Complementary Angles
c)
Substitution Property
d)
Definition of Supplementary Angles
43.
What is the missing statement in the proof?
a)
Addition Property of Equality
b)
Segment Addition Postulate
c)
Substitution Property of Equality
d)
Transitive Property
44.
A mathematical statement that requires proof is a
a)
theorem
b)
postulate
c)
definition
d)
conjecture
45.
A rule that is accepted without proof
a)
postulate
b)
theorem
c)
proof
d)
conditional statement
46.
What are the next number in this pattern?
1, 3, 6, 10, 15, ___
a)
32
b)
20
c)
0
d)
21
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