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Geometry Chapter 2 Review

Total questions: 79

Worksheet time: 2hrs 43mins

Name
Class
Date
1.

Which of the following is true about the conditional statement below?

If a man is 7 feet tall, then he plays basketball.

a)

Hypothesis: a man is 7 feet tall

Conclusion: he plays basketball

b)

Hypothesis: IF a man is 7 feet tall

Conclusion: THEN he plays basketball

c)

Hypothesis: THEN he plays basketball

Conclusion: IF a man is 7 feet tall

d)

Hypothesis: he plays basketball

Conclusion: a man is 7 feet tall

2.

Which of the following is true about the conditional statement below?

If you are flying, then you are in a

jet.

a)

Hypothesis: you are flying

Conclusion: you are in a

jet

b)

Hypothesis: IF you are flying

Conclusion: THEN you are in a

jet

c)

Hypothesis: THEN you are in a

jet

Conclusion: IF you are flying

d)

Hypothesis: you are in a

jet

Conclusion: you are flying

3.

Which of the following is a valid conditional statement for the following phrase:

An acute angle has a measure less than 90°.

a)

If an angle is acute, then it has a measure less than 90°.

b)

If an angle is not acute, then it does not have a measure less than 90°.

c)

If an angle is acute, then it is acute.

d)

If an angle does not measure less than 90°, then it is not acute.

4.

Name the figure.

(Select all that apply)

a)

PV‾\overline{PV}  

b)

PV→\overrightarrow{PV}  

c)

T←P→\overleftarrow{T}\overrightarrow{P}  

d)

P←V→\overleftarrow{P}\overrightarrow{V}  

5.

Name the figure.

(Select all that apply)

a)

OM→\overrightarrow{OM}  

b)

MO→\overrightarrow{MO}  

c)

MV→\overrightarrow{MV}  

d)

OV→\overrightarrow{OV}  

6.

Name the angle shown.

(Select all that apply)

a)

∠Q\angle Q  

b)

∠SQR\angle SQR  

c)

∠RSQ\angle RSQ  

d)

∠RQS\angle RQS  

7.

Which angles are properly named?

a)

∠Q\angle Q  

b)

∠P\angle P  

c)

∠S\angle S  

d)

∠R\angle R  

8.

Name the angle.

(Select all that apply)

a)

∠S\angle S  

b)

∠RST\angle RST  

c)

∠TSR\angle TSR  

9.

Which of the following statements is incorrect?

a)

BC‾=DC‾\overline{BC}=\overline{DC}  

b)

mBC‾=mDC‾m\overline{BC}=m\overline{DC}  

c)

BC‾≅DC‾\overline{BC}\cong\overline{DC}  

10.

Which of the following statements are correct?

a)

∠C=∠A\angle C=\angle A  

b)

m∠C=m∠Am\angle C=m\angle A  

c)

∠C≅∠A\angle C\cong\angle A  

11.

Which of the following angles is not in the figure?

a)

∠TUW\angle TUW  

b)

∠VUW\angle VUW  

c)

∠VWT\angle VWT  

d)

∠TUV\angle TUV  

12.

Name the figure.

(Select all that apply)

a)

CL→\overrightarrow{CL}  

b)

AL→\overrightarrow{AL}  

c)

CA→\overrightarrow{CA}  

13.

Name the figure.

(Select all that apply)

a)

J←A→\overleftarrow{J}\overrightarrow{A}  

b)

A←W→\overleftarrow{A}\overrightarrow{W}  

c)

J←W→\overleftarrow{J}\overrightarrow{W}  

14.

.

.

What kind of intersecting lines are these?

a)

Parallel Lines

b)

Perpendicular Lines

c)

adjacent

d)

opposite

15.

What is a line segment?

a)

Part of a line with that connects 2 points

b)

Part of a line that has 1 point

c)

A line that goes on without end

d)

Part of a line with 5 points

16.

What is a ray?

a)

Part of a line with 2 points

b)

Part of a line with 1 point and goes on forever

c)

Part of a line with 0 points

d)

Part of a line with 5 points

17.

This symbol,→ , means?

a)

and

b)

or

c)

not

d)

if, then

18.

What symbol is a negation?

a)

∨

b)

∧

c)

→

d)

~

19.

A counterexample is an example that proves a conjecture to be true.

a)

True

b)

False

20.

To fully disprove a conjecture, one needs to find only ONE counterexample.

a)

True

b)

False

21.

Which of the following is a counterexample to the following conjecture? If x2 = 4x^2\ =\ 4 , then x = 2

a)

x = 4

b)

x = -2

c)

x = 2

d)

x = -4

22.
If an animal is furry, then it is a hamster. What would be an appropriate counterexample?
a)
goldfish
b)
frog
c)
elephant
d)
cat
23.
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
24.

Which of the following provide a counterexample to the claim:

"If two angles are supplementary, then they are not congruent."

a)

40° and  140°40\degree\ and\ \ 140\degree

b)

80° and  80°80\degree\ and\ \ 80\degree

c)

30° and  150°30\degree\ and\ \ 150\degree

d)

90° and  90°90\degree\ and\ \ 90\degree

25.
Determine whether the stated conclusion is valid.
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.
a)
Invalid
b)
Valid
c)
Sammy is a Great Dane
d)
Sammy is really a cat.
26.
Draw a conclusion from the statement.
If you live in Orlando, then you live in Florida.
You live in Orlando.
a)
You live in Disney Land
b)
You are an old person.
c)
You live in Florida
d)
You live in Orlando
27.
Draw a conclusion from the statement.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.
a)
Then it's not odd.
b)
Then it's a whole number.
c)
Then its square is divisible by 4
d)
Then it's even.
28.
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
29.

If the sun is shining it is a beautiful day. If it is a beautiful day then we will go go hiking.

a)

If the sun is not shining, we will not go hiking.

b)

If the sun is shining then we will go hiking.

c)

No conclusion can be made.

d)

If we go hiking, then it is a beautiful day.

30.

If you go to the swimming pool, then you will enjoy yourself. If you enjoy yourself, you will want to return.

a)

If you return to the pool you will enjoy yourself.

b)

If you enjoy yourself, then you went to the pool.

c)

If you go to the pool, you will want to return.

d)

No conclusion can be made.

31.

What property of equality is shown below?

25 + d = 36

25 + d - 25 = 36 - 25

a)

addition property of equality

b)

subtraction property of equality

c)

division property of equality

d)

multiplication property of equality

32.

What property of equality is shown below?

y - 12 = 30

y -12 + 12 = 30 +12

a)

addition property of equality

b)

subtraction property of equality

c)

multiplication property of equality

d)

division property of equality

33.

What property of equality is shown below?
7n=28
7n ÷\div  7 = 28  ÷\div  7

a)

addition property of equality

b)

subtraction property of equality

c)

multiplication property of equality

d)

division property of equality

34.

if a=b, then b=a

a)

symmetric

b)

reflexive

c)

transitive

d)

substitution

35.

if a=b, and b=c, then a=c (the only 3 eq. property)

a)

transitive

b)

reflexive

c)

symmetric

d)

substitution

36.

if a(b+c)=ab+ac, then ab+ac=a(b+c)

a)

distributive

b)

substitution

c)

Associative

d)

communitive

37.

Identify this property.

If j = k, then k = j.

a)
Symmetric
b)
Reflexive
c)
Transitive
d)

Addition Property of Equality

38.
Fill in the reason for number 5. 
a)
Definition of congruent angles
b)
Angle Addition Postulate
c)
Substitution Property
d)
Transitive Property
39.
Which is the correct reason for statements 2 and 4 in the proof?
a)
Corresponding Angles
b)
Substitution
c)
Definition of Congruent Angles
d)
Vertical Angles are congruent.
40.
Which property justifies the next step?
a)
Definition of linear pair
b)
Definition of supplementary angles
c)
Congruent supplements thm
d)
Linear pair postulate
41.
What is the reason?
a)
Transitive 
b)
Substitution
c)
Middle Man
d)
Replacing 
42.
What is the REASON for Statement #2?
a)
Given
b)
Definition of Complementary Angles
c)
Substitution Property
d)
Reflexive Property of Congruence
43.

1) Which statement restates the Given from the question?

a)
b)
c)
44.

Which of the following is true about the conditional statement below?

If a man is 7 feet tall, then he plays basketball.

a)

Hypothesis: a man is 7 feet tall

Conclusion: he plays basketball

b)

Hypothesis: IF a man is 7 feet tall

Conclusion: THEN he plays basketball

c)

Hypothesis: THEN he plays basketball

Conclusion: IF a man is 7 feet tall

d)

Hypothesis: he plays basketball

Conclusion: a man is 7 feet tall

45.

Which of the following is the CONVERSE of the statement below?

If an object is a bird, then it can fly.

a)

If an object can fly, then it is a bird.

b)

If an object is not a bird, then it cannot fly

c)

If an object cannot fly, then it is not a bird

d)

There is no converse of the statement

46.
Write the following statement in if-then form.
All students at Hermitage take an English class.
a)
If you take an English class, then you are a student at Hermitage.
b)
If you are a student at Hermitage, then you take an English. class
47.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle does not have a measure less than 90°, then it is not acute.

a)

Contrapositive

b)

Converse

c)

Biconditional

d)

Inverse

48.
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
49.
What is a conjecture?
a)
A statement believed to be true based on observations.
b)
An example which disproves an hypothesis.
c)
the performance of tricks that are seemingly magical
50.
Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, then...
a)
Look out for the snowplows while driving to school.
b)
The big test will not be given today.
c)
The roads will be hard to drive on.
d)
You should call the school to see if school is canceled.
51.
p→q
q→r
∴p→r
Which law is modeled?
a)
Law of Syllogism
b)
Law of Detachment
c)
Law of Contrapositive
d)
Law of Shannon
52.
If an angle is 40⁰, then it is acute.
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?
a)
∠A is complementary to ∠B
b)
∠A is acute.
c)
∠A is obtuse.
d)
∠A is 40⁰
53.

Can you assume the following is true based on the diagram:

Planes L and K intersect at Line PS?

a)

Yes

b)

No

54.

Can you assume the following is true based on the diagram:

Line MQ is in Plane L

a)

Yes

b)

No

55.

Which reason justifies the statement?

a)

Subtraction Property of Equality

b)

Combine Like Terms

c)

Division Property of Equality

d)

Addition Property of Equality

56.

Which reason justifies the statement?

a)

Addition Property of Equality

b)

Multiplication Property of Equality

c)

Subtraction Property of Equality

d)

Division Property of Equality

57.

Which reason justifies the statement?

a)

Combine Like Terms

b)

Distributive Property

c)

Multiplication Property of Equality

d)

Division Property of Equality

58.
Step 1 is what
a)
addition property of equality
b)
given
c)
subtraction property of equality
d)
prove
59.
What is reason 5?
a)
Transitive Property
b)
Reflexive Property
c)
Symmetric Property
d)
Prove
60.
What is reason 3?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
61.

What is the relationship between <EAD and <DAC?

a)

They are a linear pair.

b)

They are complementary.

c)

They are supplementary.

d)

They are Vertical.

62.

The conclusion from this diagram is that angle 1 and angle 2 are a linear pair.

What's the reason for this conclusion?

a)

m∠1+m∠2=180m\angle1+m\angle2=180

b)

Definition of linear pair

c)

Linear pair postulate

d)

definition of supplementary

63.

Which option best fills in the blank in the proof?

a)

Substitution Property

b)

Definition of Linear Pair

c)

Definition of Supplementary Angles

d)

Angle Addition Postulate

64.
What is a conjecture?
a)
A statement believed to be true based on observations.
b)
An example which disproves an hypothesis.
c)
the performance of tricks that are seemingly magical
65.
What are the next two numbers in this pattern?
12, 17, 22, 27, ___, ___
a)
32, 37
b)
30, 37
c)
30, 33
d)
32, 35
66.
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
67.

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

a)

Inductive

b)

Deductive

68.
All bears are mammals, all mammals have kidneys; therefore all bears have kidneys. 
a)
Deductive
b)
Inductive
69.
All observed houses on South Street have roofs that are falling apart.  Sherry lives on South Street.  Her roof is falling apart. 
a)
Deductive
b)
Inductive
70.

Is Inductive or Deductive reasoning used in this situation?


The catalog states that all incoming freshman must take the math placement exam.

You are an entering freshman.

Therefore you must take the math placement exam.

a)

Inductive

b)

Deductive

71.

Consider the following statement.

If a figure is a square, then it has four sides.

New Statement: If the figure is not a square, then it does not have four sides.

What does the new statement represent?

a)

converse

b)

inverse

c)

contrapositive

72.

Consider the following statement.

If a figure is a square, then it has four sides.

New Statement: If the figure does not have four sides, then it is not a square.

What does the new statement represent?

a)

converse

b)

inverse

c)

contrapositive

73.

Consider the following statement.

If a figure is a square, then it has four sides.

New Statement: If the figure has four sides, then it is a square.

What does the new statement represent?

a)

converse

b)

inverse

c)

contraspositive

74.

Fill in the reason that justifies the step to solve for x in the diagram.

Given: QS = 42

Step: QR + RS = QS

a)

Division Property of Equality

b)

Segment Addition Postulate

c)

Simplify or CLT

75.

Find the value of the variable.

a)

2

b)

18

c)

1⁄2

d)

4 1⁄2

76.

Find the value of the variable.

a)

8 3⁄4

b)

25

c)

20

d)

40

77.

m∠3 = 57. Find m∠1.

a)

123

b)

133

c)

57

d)

47

78.

Find the values of x and y.

a)

x = 51, y = 129

b)

x = 129, y = 51

c)

x = 42, y = 17

d)

x = 17, y = 42

79.

What are the values of x and y?

a)

x=-7;y=5

b)

x=-10;y=-3

c)

x=33, y=147

d)

x=10; y=-3

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