Free Printable Practice Questions on UNIT 3A

1.

Using the statements:
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.

a)

It is not Friday

b)

It is Friday

c)

I will not get paid

d)

I will get paid

2.

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.

3.

Which is a valid conclusion from these statements?
If a quadrilateral is a rhombus, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

a)

Opposite angles of a quadrilateral are congruent

b)

Opposite angles of a rhombus are congruent

c)

Every quadrilateral is a rhombus

d)

Every parallelogram is a rhombus

4.

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

5.

Use Law of Syllogism to make a conclusion.
If a number is divisible by 10, then it is divisible by 2. If a number is divisible by 2, then it is even.

a)

If a number is divisible by 10, then it is even,

b)

If a number is even, then it is divisible by 10.

c)

If a number is divisible by 2, then it is even.

d)

If a number is even, then it is divisible by 2.

6.

Using the Law of Detachment, what can you conclude?
If x has a value of 4, then 2x has a value of 8.
The value of x is 4.

a)

x = 4

b)

no conclusion can be made

c)

2x does not have a value of 8

d)

2x has a value of 8

7.

Write the if-then statement that follows from the pair of true statements. If the sun is shining, then it is a beautiful day. If it is a beautiful day, then we will have a picnic.

a)

If the sun is shining, then it is a beautiful day.

b)

If it is a beautiful day, then the sun is shining.

c)

If the sun is shining, then we will go on a picnic.

d)

If we go on a picnic, then the sun is shining.

8.

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

a)

If Tom goes fishing then he catches a fish.

b)

If Tom brings his pole then he goes fishing

c)

If Tom catches a fish then he brought his pole.

d)

If Tom brings his pole then he catches a fish.

9.

Write the if-then statement that follows from the pair of true statements. If Todd goes to the movies, then Sarah will go to the movies. If Chris goes to the movies, then Todd will go to the movies.

a)

If Chris goes to the movies, then Sarah will go to the movies.

b)

If Todd goes to the movies, then Chris will go to the movies.

c)

If Sarah goes to the movies, then Chris will go to the movies.

d)

If Chris goes to the movies, then Todd will go to the movies.

10.

Which of the following statements is valid based on the given scenario?
If Jason plays basketball, then Steve sits on the bench.
If Steve sits on the bench, then Ronald starts at center.

a)

If Steve sits on the bench then Jason plays basketball.

b)

If Ronald starts at center then Jason plays basketball.

c)

If Steve sits the bench then Ronald does not start at center.

d)

If Jason plays basketball then Ronald starts at center.

11.

By the Law of Detachment, what can you conclude from the statement?
If two planes intersect, then their intersection is a line.
Planes S and T intersect.

a)

their intersection is a line

b)

their intersection is a point

c)

no conclusion can be made

d)

the planes are parallel

12.

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 Los Angeles, then you are in California.
Conjecture: If you are in Los Angeles, then you are in the west coast.

a)

No, the conjecture is not valid.

b)

Yes, the conjecture is valid.

13.

Use the Law of Detachment to determine what you can conclude from the given information, if possible.

If you passed the final, then you pass the class. You passed the final.

a)

You passed the class.

b)

You didn't pass the class

c)

Not possible

14.

Use the Law of Detachment to determine what you can conclude from the given information, if possible.

If your parents let you borrow the car, then you will go to the movies with your friend. If you went to the movies with your friend, that means that....

a)

Your parents let you borrow the car.

b)

Your parents didn't let you borrow the car.

c)

Not possible

d)

You and your friends bought popcorn

15.

If the school cafeteria sells pizza today, Greg is going to eat four pieces. Pizza is on sale for school lunch today.

Using deductive reasoning, what statement can you make based on this information?

a)

Lots of people will buy pizza.

b)

The school cafeteria sells pizza.

c)

Greg will eat four pieces of pizza.

d)

Greg needs to go on a diet.

16.

What can be concluded from the following statements?

If Mike rakes leaves, then he bags them .

If Mike bags the leaves then he mows the lawn.

a)

If Mike mows the lawn then he bags the leaves.

b)

If Mike bags the leaves then he rakes.

c)

If Mike rakes the leaves then he will mow the lawn

d)

If Mike does not mow the lawn then he cannot bag the leaves

17.

What conclusion can be drawn from the following statements?
If the stereo is on, then the volume is loud.
If the volume of the stereo is loud, then the neighbors will complain.

a)

If the neighbors complain, then the stereo will be loud.

b)

If the stereo is on, then the neighbors will complain.

c)

If the stereo is volume is loud, then the stereo is on.

d)

If the stereo is on, then the volume is loud.

18.

IF All even numbers are divisible by 2

AND 28 is even

THEN

a)

2 is an even number

b)

28 is divisible by 2

c)

All numbers are divisible by 2

d)

All numbers are even numbers

19.

IF an apple a day keeps the doctor away.

AND Joe ate an apple every day.

THEN

a)

He will get a stomach ache

b)

This makes no sense, what do apples have to do with doctors?

c)

Joe will be spending lots of time at the dentists office

d)

The doctor will stay away

20.

Jason and Jackson are in a band

The band plays on Saturday night

The band goes on at 8:00 pm

Conclusion:

a)

Jason and Jackson need to get girlfriends to watch them play

b)

It is Saturday night

c)

On Saturday night at 8:00 Jason and Jackson will be performing

d)

The time is 8:00 pm and the crowd is yelling

21.

Given the diagram, which is correct?

a)

BC+CD=BD

b)

BD+BC=CD

c)

CD+BC=BD

d)

BC+BD=CD

22.

Find ST.

a)

11

b)

12

c)

13

d)

14

23.

Find the length of DE

a)

58

b)

6

c)

36

d)

61

24.

Find AC

a)

8.5

b)

9.5

c)

25.5

d)

10

25.

Find MK.

a)

6

b)

4

c)

14

d)

8

26.

Given that R is between S and T.
RS=6, TR=4.5, TS= ______

a)

1.5

b)

10.5

c)

6

d)

4.5

27.

What does the word BISECT mean?

a)

To cut something into more than five pieces.

b)

It is a plane with two sets of wings.

c)

A shape that has three sides.

d)

To cut something into two congruent pieces or in half.

28.

This point divides a line segment into 2 equal parts.

a)

point

b)

vertex

c)

midpoint

d)

angle

29.

Find the value of r if M is the midpoint of JK. (worksheet)

a)

r=64

b)

r=32

c)

r=3

d)

r=1/3

30.

a)

MQ=4, PQ=8

b)

MQ=4, PQ=4

c)

MQ=8, PQ=4

d)

MQ=8, PQ=8

31.

B is the midpoint of AC. Find AB.

a)

2

b)

16

c)

8

d)

4

32.

a)

12

b)

62

c)

35

d)

9

33.

RM=

a)

RM=6 MS=6

b)

RM=3 MS=3

c)

RM=3 MS=6

d)

RM=12 MS=6

34.

RS is the segment bisector. If OQ = 32 and PO = 4x, what does x equal?

a)

8

b)

28

c)

128

d)

36

35.

M is the midpoint of AB. If AM = 5x+10 & MB = 4x+16, find the value of AM.

a)

6

b)

4

c)

70

d)

40

36.

The angle relationship shown is -

a)

complementary angles

b)

supplementary angles

c)

vertical angles

d)

adjacent angles

37.

Which equation can be used to determine the value of x?

a)

2x + 10 = 46

b)

2x + 10 + 46 = 180

c)

2x + 10 + 46 = 90

d)

not here

38.

$m\angle2=34\degree$

Find $m\angle3$ and state the theorem used

a)

$m\angle3=56\degree$ Supplement Theorem

b)

$m\angle3=66\degree$ Supplement Theorem

c)

$m\angle3=56\degree$ Complement Theorem

d)

$m\angle3=66\degree$ Complement Theorem

39.

What is the reason?

a)

Reflexive

b)

Symmetric

c)

Definition of congruence

d)

Definition of equal

40.

Which property justifies the next step?

a)

Symmetric Property

b)

Transitive Property

c)

Segment Addition Property

d)

Reflexive Property

41.

Find m∠3. ∠2 and ∠3 are complementary. ∠1≅ ∠4 and m∠2 = 28.

a)

62°

b)

45°

c)

28°

d)

72°

42.

Find m∠13 if m∠11 = 11x and m∠13 = 10x + 12. Then determine which theorem justifies your work.

a)

92°, Supplement Theorem

b)

92°, Vertical Angles Theorem

c)

88°, Supplement Theorem

d)

88°, Vertical Angles Theorem

43.

For any numbers a and b, if a = b, then b = a.

a)

Transitive Property

b)

Reflexive Property

c)

Symmetric Property

d)

Substitution Property

44.

Name the property described:
If MN = OP and OP = QR, then MN = QR

a)

Reflexive

b)

Symmetric

c)

Transitive

d)

Addition

45.

Find the value of x.

a)

52

b)

63

c)

53

d)

58

46.

Given: <1 and <3 are vertical angles. What should you conclude by the vertical angles theorem?

a)

<1 and <2 are a linear pair

b)

<1 and <3 are right angles

c)

<2 and <4 are vertical angles

d)

$<1\cong<3$

47.

What is the justification?

a)

Symmetric Prop.

b)

Angle addition postulate

c)

Reflexive Prop

d)

Transitive Prop.

48.

$\angle1+\angle2=\angle ADC$
What theorem/postulate was used?

a)

Vertical Angles Theorem

b)

Angle Addition Postulate

c)

Segment Addition Postulate

d)

Congruent Supplements Theorem

49.

Given that C is between A and B, which Segment Addition statement is correct?

a)

AC + AB = CB

b)

AC + CB = AB

c)

AB + BC = AC

d)

CA + CB = CA

50.

Part of a line. Has one endpoint and continues on forever in one direction.

a)

Line Segment

b)

Line

c)

Ray

d)

Point

51.

Find HG.

a)

8

b)

9

c)

10

d)

11

52.

Find AC

a)

7

b)

8

c)

22

d)

23

53.

Use the figure to write and solve an equation for x.

a)

5

b)

6

c)

7

d)

8

54.

a)

MQ=4, PQ=8

b)

MQ=4, PQ=4

c)

MQ=8, PQ=4

d)

MQ=8, PQ=8

55.

a)

12

b)

62

c)

35

d)

9

56.

What does the word BISECT mean?

a)

To cut something into more than five pieces.

b)

It is a plane with two sets of wings.

c)

A shape that has three sides.

d)

To cut something into two congruent pieces or in half.

57.

This point divides a line segment into 2 equal parts.

a)

point

b)

vertex

c)

midpoint

d)

segment

58.

B is the midpoint of AC. Find AB.

a)

2

b)

16

c)

8

d)

4

59.

RS is the segment bisector. If OQ = 32 and PO = 4x, what does x equal?

a)

8

b)

28

c)

128

d)

36

60.

Line e is a "segment bisector" of AB at point M.

If AM = 4n-40 & MB = 14 - 14n, find the value of n.

a)

7

b)

3

c)

5

61.

Find the value of x.

a)

150

b)

30

c)

145

d)

15

62.

Find $m\angle AEB.$

a)

150

b)

30

c)

130

d)

50

63.

Find the value of x.

a)

28

b)

30

c)

32

d)

90

64.

Find $m\angle ECD$

a)

13

b)

64

c)

90

d)

180

65.

Find the value of x.

a)

18.75

b)

21.25

c)

80

d)

158.75

66.

Find $m\angle AED.$

a)

10

b)

14

c)

52

d)

128

67.

Find the value of y.

a)

16

b)

32

c)

38

d)

142

68.

Find $m\angle A$ if $\angle A$ is congruent to its supplement, $\angle B.$

a)

45

b)

90

c)

180

d)

impossible to determine

69.

Find $m\angle A$ if $\angle A$ is twice as large as its complement, $\angle B.$

a)

30

b)

45

c)

60

d)

90

70.

Which property justifies the next step?

a)

Symmetric Property

b)

Segment Addition Postulate

c)

Definition Midpoint

d)

Definition Congruence

71.

Which property justifies the next step?

a)

Symmetric Property

b)

Transitive Property

c)

Segment Addition Property

d)

Reflexive Property

72.

Name the property, definition, postulate, or theorem.

a)

def of congruent segments

b)

def of midpoint

c)

Segment Add Post

d)

def of angle bisector

73.

For any numbers a and b, if a = b, then b = a.

a)

Transitive Property

b)

Reflexive Property

c)

Symmetric Property

d)

Substitution Property

74.

Name the property described:
If PQ = RS then RS = PQ

a)

Reflexive

b)

Symmetric

c)

Transitive

d)

Addition

75.

AB + BC = AC is justified by which option below?

a)

Angle Addition Postulate

b)

Addition Property

c)

Segment Addition Postulate

d)

Theorem 22C

76.

∠1 and ∠3 can best be described as -

a)

complementary angles

b)

supplementary angles

c)

vertical angles

d)

adjacent angles

77.

Which equation can be used to determine the value of x?

a)

2x + 10 = 46

b)

2x + 10 + 46 = 180

c)

2x + 10 + 46 = 90

d)

not here

78.

Find the value of x.

a)

52

b)

63

c)

53

d)

58

79.

Find the value of x.

a)

19

b)

15

c)

14

d)

11

80.

Given: <1 and <3 are vertical angles. What should you conclude by the vertical angles theorem?

a)

<1 and <2 are a linear pair

b)

<1 and <3 are right angles

c)

<2 and <4 are vertical angles

d)

$<1\cong<3$

81.

What kind of angles are $\angle1\ and\ \angle2$ ?

a)

Exterior angles

b)

Vertical angles

c)

A Linear Pair

d)

Corresponding angles

e)

Alternate Interior angles

82.

What type of angles are these?

a)

Adjacent Angles

b)

Linear Pair

c)

Complementary Angles

d)

Supplementary Angles

e)

Vertical Angles

83.

Which angles are vertical angles?

a)

$\angle8\ \ and\ \angle7$

b)

$\angle8\ and\ \angle6$

c)

$\angle8\ and\ \angle5$

84.

Which angle is a linear pair with $\angle1$ ?

a)

$\angle2$

b)

$\angle3$

c)

$\angle4$

d)

$\angle5$

e)

$\angle6$

85.

Which angle is a vertical angle to with $\angle7$ ?

a)

$\angle1$

b)

$\angle5$

c)

$\angle3$

d)

$\angle6$

e)

$\angle9$

86.

Find the missing angle. Find x.

a)

20^o

b)

70^o

c)

160^o

d)

180^o

87.

a)

x = 118

b)

x = 108

c)

x = 28

d)

x = 58

e)

x = 62

88.

Find m∠13 if m∠11 = 11x and m∠13 = 10x + 12. Then determine which theorem justifies your work.

a)

92°, Supplement Theorem

b)

92°, Vertical Angles Theorem

c)

88°, Supplement Theorem

d)

88°, Vertical Angles Theorem

89.

Find the value of x.

a)

19

b)

15

c)

14

d)

11

90.

Given: <1 and <3 are vertical angles. What should you conclude by the vertical angles theorem?

a)

<1 and <2 are a linear pair

b)

<1 and <3 are right angles

c)

<2 and <4 are vertical angles

d)

$<1\cong<3$

91.

What is the justification?

a)

Symmetric Prop.

b)

Angle addition postulate

c)

Reflexive Prop

d)

Transitive Prop.

92.

B is the midpoint of AC. Find AB.

a)

2

b)

16

c)

8

d)

4

93.

What does the word BISECT mean?

a)

To cut something into more than five pieces.

b)

It is a plane with two sets of wings.

c)

A shape that has three sides.

d)

To cut something into two congruent pieces or in half.

94.

Angle A and B are complementary. If $\angle A=2\left(3x-6\right)$ and $\angle B=6\left(x-1\right)$ what is $m\angle B$ ?

a)

6

b)

24

c)

48

d)

11

95.

Name the property of equality that the statement illustrates.

If ∠S and ∠P are supplementary, then m∠S + m∠P = 180°

a)

Definition of Supplementary Angles

b)

Definition of Complementary Angles

c)

Definition of Linear Pair

d)

Definition of Vertical Angles

96.

In symmetric property: If $\angle A\cong\angle B$ , then

a)

$\angle B\cong\angle A$

b)

$\angle A\cong\angle A$

c)

$\angle A+\angle B=\angle C$

d)

$\angle B\cong\angle B$

97.

If $\angle D\cong\angle E\ and\ \angle F\cong\angle D$ , then

a)

$\angle D\cong\angle F$

b)

$\angle E\cong\angle F$

c)

$\angle D\cong\angle D$

d)

$\angle D+\angle E\cong\angle F$

98.

If $\angle X\ and\ \angle Y$ are vetical, then

a)

$\angle X+\angle Y\ =\angle Z$

b)

$\angle X\cong\angle Y$

c)

they are complementary.

d)

they are suppkementary.

99.

$\angle D\ and\ \angle E\ are\ \ complementary.\$

$m\angle D=3x+1\ and\ m\angle E=2x+4,\ find\ x.$

a)

90

b)

15

c)

16

d)

17

100.

What ray is the bisector of $\angle AOC$ ?

a)

$\overrightarrow{OB}$

b)

$\overrightarrow{OC}$

c)

$\overrightarrow{BO}$

d)

$\overline{OB}$

101.

If $\overrightarrow{KM}$ bisects $\angle LKJ$ and $m\angle JKM=22\degree$ find $m\angle LKM$ .

a)

22

b)

44

c)

11

d)

68

e)

not enough information given

102.

What kind of angles are $\angle1\ and\ \angle2$ ?

a)

Exterior angles

b)

Vertical angles

c)

A Linear Pair

d)

Corresponding angles

e)

Alternate Interior angles

Practice Questions on UNIT 3A

Total questions: 102

Worksheet time: 6hrs 43mins

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