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Reasoning and angle pairs Review

Total questions: 101

Worksheet time: 19hrs 22mins

Name
Class
Date
1.
Which value of x will show that lines l and m are parallel?
a)
20
b)
22
c)
24
d)
25
2.
What value of x proves that line p is parallel to line r?
a)
14
b)
12.5
c)
15
d)
25
3.
If a // b and c // d in the figure below, then what is the value of x?
a)
47
b)
57
c)
133
d)
143
4.
Which of the following relationship proves that j is parallel to k?
a)
∠3 and ∠4 are supplementary
b)
∠4 and ∠5 are supplementary
c)
∠1 ≅ ∠3
d)
∠2 ≅ ∠3
5.
Line v is a transversal.  Which is a true statement?
a)
w // x and x // y
b)
w // x and y // z
c)
w // y and x // z
d)
w // z and x // y
6.
Which condition will prove that line l is parallel to line m?
a)
∠1 ≅ ∠3
b)
∠3 ≅ ∠5
c)
∠1 ≅ ∠6
d)
∠6 ≅ ∠5
7.
Line l and m are intersected by transversal n.  Which statement proves that line l is parallel to line m?
a)
∠2 ≅ ∠3
b)
∠2 ≅ ∠6 
c)
m∠7 + m∠8 = 180°
d)
m∠3 + m∠5 = 90°
8.
What is the value of x?
a)
13
b)
48
c)
132
d)
60
9.
Angles x and y are....
a)
alternate interior
b)
alternate exterior
c)
corresponding
d)
consecutive interior
10.
A line is perpendicular to    y = 2x - 7.
What is the slope of this line? 
a)
-2
b)
1/2
c)
-1/2
d)
2
11.
y = 3x +2
y = 3x - 3
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
d)
The same line
12.
Slopes of parallel lines are...
a)
opposite reciprocals.
b)
opposites.
c)
the same.
d)
always 7.
13.
Slopes of perpendicular lines are...
a)
opposite reciprocals.
b)
opposites.
c)
the same.
d)
always 7.
14.

Classify the relationship between the pair of angles. ∠7 and ∠10

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

None

15.

Classify the relationship between the pair of angles. ∠2 and ∠13

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

None

16.

Classify the relationship between the pair of angles. ∠2 and ∠3

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

None

17.

What is the value of y in the figure?

a)

8

b)

20

c)

25

d)

10

18.

What is the value of x in the figure?

a)

5

b)

7

c)

12

d)

20

19.

What is the value of y in the figure?

a)

5

b)

7

c)

12

d)

20

20.

Select the figure that makes lines r and t parallel.

a)
b)
c)
d)
21.

Which graph would be parallel to the graph of the equation y = - ⅔ x + 20

a)
b)
c)
d)
22.
Name the angle relationship.
a)
Alternate Interior
b)
Alternate Exterior
c)
Corresponding
d)
Vertical Angles
23.
Name the angle relationship.
a)
Alternate Interior
b)
Alternate Exterior
c)
Corresponding
d)
Vertical Angles
24.
Name the angle relationship.
a)
Consecutive Interior
b)
Alternate Interior
c)
Corresponding
d)
Vertical Angles
25.

What is the measure of ∠8 if the lines are parallel?

a)

55°55\degree  

b)

155°155\degree  

c)

135°135\degree  

d)

45°45\degree  

26.
If angle 4 is x + 15 and angle 2 is 3x - 5, what is the value of x?
a)
5
b)
10
c)
25
d)
x + 15
27.
Find m∠ADE. 
a)
77°
b)
93°
c)
110°
d)
80°
28.
A part of a line that has one endpoint and goes on forever in the other direction
a)
Line
b)
Ray
c)
Line Segment
d)
Angle
29.
2 rays make up a(n)
a)
ray
b)
line segment
c)
line
d)
angle
30.
Which pair of angles must be supplementary so that r is parallel to s?
a)
∠2 and ∠3
b)
∠5 and ∠6
c)
∠4  and ∠10
d)
∠6  and ∠14
31.
What is the value of x?
a)
22
b)
26
c)
24
d)
23
32.
WHAT IS THE CORRECT EQUATION TO FIND THE VALUE OF X?
a)
X=12
b)
8X - 17 + 5X +19 = 180
c)
8X - 17 = 5X +19
d)
X= -12
33.

Solve for x

a)

80

b)

100

c)

90

d)

180

34.
What value of x proves that line p is parallel to line r?
a)
14
b)
12.5
c)
15
d)
25
35.

Find x.

a)

x = 29

b)

x = -13

c)

x = 20

d)

x = 3

36.
What is the measure of ∠ABC?
a)
25°
b)
75°
c)
108°
d)
150°
37.
If angle 6 is 25 degrees, how many degrees is angle 7?
a)
25 degrees
b)
50 degrees
c)
90 degrees
d)
155 degrees
38.
What are vertical angles?
a)
Angles that are adjacent to each other
b)
Angles that add up to 180°
c)
Angles that are opposite of each other when lines intersect
d)
Angles that add up to 90°
39.

Which of the statements below can be concluded from the diagram?

a)

c⊥dc\perp d

b)

b∥ab\parallel a

c)

b∥cb\parallel c

d)

a⊥ba\perp b

40.

Which of the statements below can be concluded from the diagram?

a)

c⊥dc\perp d

b)

b∥ab\parallel a

c)

d∥cd\parallel c

d)

a⊥ca\perp c

41.

Which of the statements below can be concluded from the diagram?

a)

c⊥bc\perp b

b)

b∥ab\parallel a

c)

d∥bd\parallel b

d)

a⊥ca\perp c

42.

Two intersecting lines are always coplanar.

a)

True

b)

False

43.

Parallel lines are cut by a transversal. Which pair of resulting angles are NOT always congruent?

a)

Corresponding angles

b)

Alternate exterior angles

c)

Alternate interior angles

d)

Consecutive interior angles

44.

Which statement can be used to prove that line n and line m are parallel?

a)

Angle 1 and angle 4 are congruent.

b)

Angle 3 and angle 6 are congruent.

c)

Angle 2 and angle 8 are congruent.

d)

Angle 4 and angle 7 are congruent.

45.

The measure of two vertical angles are 2x + 14 degrees and 3x + 8 degrees. What is the measure of each angle?

a)

6°6\degree  

b)

14°14\degree  

c)

24°24\degree  

d)

26°26\degree  

46.

<1 and <3 are supplementary. <1 and <2 are vertical angles. The measure of angle 3 is 59 degrees. What is the measure of angle 2?

a)

31 degrees

b)

59 degrees

c)

121 degrees

d)

131 degrees

47.

True or False: If two sides of two adjacent acute angles are perpendicular, then the angles are complimentary.

a)

True

b)

False

48.

Which of the following angle measures is NOT true for this diagram?

a)

m<4 = 30 degrees

b)

m<1 = 90 degrees

c)

m<5 = 90 degrees

d)

m<2 = 60 degrees

49.

Identify which conclusions can be made from the picture?

a)

segment AB and segment CD are parallel, but segment AZ and segment FG are not parallel.

b)

segment AB and segment AZ are parallel, while segment CD and segment FG are perpendicular.

c)

segment AB and segment FG are parallel.

d)

segment AZ and CD are perpendicular.

50.

If you are told line j is not parallel to line k, which of the following statements would disprove this?

a)

<1 and <9 are supplementary

b)

<6 and <4 are supplementary

c)

<5 and <8 are congruent

d)

<12 and <1 are congruent

51.

Which two angles are supplementary

a)

∠1 and ∠3

b)

∠2 and ∠6

c)

∠4 and ∠6

d)

∠7 and ∠8

52.

What is the vertical angle of angle 4?

a)

<1

b)

<2

c)

<3

d)

<5

53.

What is the vertical angle of angle 7?

a)

<5

b)

<6

c)

<

d)

<8

54.

Are angles 1 and 3 congruent to each other?

a)

No, because they are supplementary.

b)

No, because they are vertical.

c)

Yes, because they are next to each other.

d)

Yes, because they are on the same line.

e)

Not enough information

55.

Are angles 2 and 7 congruent to each other?

a)

No, because they are on opposite sides.

b)

No, because they are alternate interior.

c)

Yes, because they are alternate interior.

d)

Yes, because they are alternate exterior.

e)

Not enough information

56.

Which pair of lines are perpendicular?

a)

x - y = 7 and y = x+3

b)

y = -4x +1 and 8x + 2y = -10

c)

y = -8 and y = 2

d)

x = 4 and y = -1

57.

If / 1= 2x + 22 and / 8 = 3x – 16, what value of x makes a || b?

a)

11

b)

17

c)

25

d)

38

58.

If / 3= 32 and / 5 = 7x + 8, what value of x makes a || b?

a)

3

b)

4

c)

7

d)

20

59.

Which lines are parallel?

a)

a || c

b)

d || e

c)

a || c and d || e

d)

a || b || c and d || e

60.

The fence below is bounded by parallel boards. Find the measure of angle 2.

a)

40°40\degree  

b)

60°60\degree  

c)

80°80\degree  

d)

120°120\degree  

61.
What is the measure of angle 1?
a)

68°68\degree  

b)

55°55\degree  

c)

112°112\degree  

d)

57°57\degree  

62.
Which property states that 4 = 4?
a)
Substitution Property
b)
Reflexive Property
c)
Symmetric Property
d)
Transitive Property
63.
Which property states that if 10a = 2b and 2b = c, then 10a = c?
a)
Substitution Property
b)
Reflexive Property
c)
Symmetric Property
d)
Transitive Property
64.
Identify the property shown.
a)
Distributive Property
b)
Commutative Property of Multiplication
c)
Associative Property of Multiplication
d)
Subtraction Property of Grouping
65.
Which property states that if 2x = 14, then x = 7?
a)
Addition Property
b)
Subtraction Property
c)
Multiplication Property
d)
Division Property
66.
Which property says that if -5x - 1 = -11, then -5x = -10?
a)
Addition Property
b)
Subtraction Property
c)
Multiplication Property
d)
Division Property
67.
Which property says if 6y = 24, then 6y - 3 = 24 - 3?
a)
Addition Property
b)
Subtraction Property
c)
Multiplication Property
d)
Division Property
68.
Which property states if 10x + w = 41 and w = 1, then 10x + 1 = 41?
a)
Substitution Property
b)
Reflexive Property
c)
Symmetric Property
d)
Transitive Property
69.
Which property says if y ÷ 2 = -10, then y = -20?
a)
Addition Property
b)
Subtraction Property
c)
Multiplication Property
d)
Division Property
70.
Which property says if 3x = 2y and 2y = z, then 3x = z?
a)
Substitution Property
b)
Reflexive Property
c)
Symmetric Property
d)
Transitive Property
71.
Which property says given 3x2 + 1, if x = 5, then 3(5)2 + 1?
a)
Substitution Property
b)
Reflexive Property
c)
Symmetric Property
d)
Transitive Property
72.
Which property says 10y = 10y?
a)
Substitution Property
b)
Reflexive Property
c)
Symmetric Property
d)
Transitive Property
73.
Which property states that 5x + 8x = x(5 + 8)?
a)
Addition Property
b)
Multiplication Property
c)
Division Property
d)
Distributive Property
74.

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 study from 6pm to 7pm tonite.

a)

I study for several hours each day.

b)

I will do well on the exam

c)

If I do well on the exam, I studied for hours.

d)

not possible

75.
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
76.

Given the conditional;

"If it snows then school will be closed"

Which is the inverse?

a)

If school is open, then it didn't snow.

b)

If school is closed, then it snowed.

c)

If it doesn't snow, then school will be open.

d)

Let it Snow!

77.

What is the contrapositive to this?

a)

If the food is not cooked, then it is not in the oven.

b)

If the food is not in the oven, then it is not cooked.

c)

If the food is cooked, then its in the oven.

d)

If food is not in the oven, then its cooked.

78.
Original: If Jenny buys a guitar, then she will not buy a keyboard.
What is this? If Jenny does buy a keyboard, then she will not buy a guitar.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
79.
Conditional: If Maria gets married, then the reception will be at the country club.
What is this statement: If the reception is at the country club, then Maria will be getting married.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
80.
To write the converse you negate both the hypothesis and the conclusion.
a)
False
b)
True
81.
Given, "If angles are congruent, then the measures of the angles are equal." Identify the conclusion.
a)
If the angles are congruent.
b)
The angles are congruent.
c)
Then the measures of the angles are equal.
d)
The measures of the angles are equal.
82.

What is it hypothesis in the statement:" If today is Tuesday, then we have school."?

a)

Tomorrow is Wednesday.

b)

We have school.

c)

Today is Tuesday.

d)

We do not have school.

83.

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

84.
When can a biconditional statement be true?
a)
When the inverse and the converse are both true
b)
When the original statement (conditional statement) & the contrapositive are both true.
c)
When the converse is true.
d)
When the original statement (conditional statement) and the converse are both true.
85.
What phrase does a biconditional statement use?
a)
if, then
b)
if, when
c)
if and only if
d)
then, if
86.
What is the biconditional that matches the statement: "A right angle is an angle with 90 degrees."
a)
If an angle has 90 degrees, then it is a right angle.
b)
If an angle is a right angle, then it has 90 degrees.
c)
An angle is a right angle if and only if it has 90 degrees.
87.

What is the correct justification for if  BD‾\overline{BD}  is the angle bisector of  ∠ABC\angle ABC  , then  ∠ABD≅∠CBD\angle ABD\cong\angle CBD  

a)

A midpoint divides a segment into two congruent segments

b)

An angle bisector divides an angle into two congruent angles

c)

All right angles are congruent

d)

Vertical angles are congruent

88.

Which reason justifies the statement if  BB  is the midpoint of  AC‾\overline{AC}  then  AB‾≅BC‾\overline{AB}\cong\overline{BC}  

a)

A midpoint divides a segment into two congruent segments

b)

An angle bisector divides an angle into two congruent angles

c)

A segment bisector intersects a segment at its midpoint

d)

Substitution 

89.

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

90.

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

a)

Inductive

b)

Deductive

91.

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

a)

Inductive

b)

Deductive

92.
Fill in the reason for number 3. 
a)
Reflexive property
b)
Symmetric Property
c)
Transitive property
d)
Substitution property
93.

The symbol ≅\cong  means..........

a)

Congruent

b)

transitive

c)

equal sign

d)

supplementary

94.

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≅<3<1\cong<3  

95.

Given: AB is the segment bisector of PQ. What conclusion can you draw?

a)

PF = QF

b)

F is the midpoint of PQ

c)

m<PFA = m<QFA

d)

<PFQ is a straight angle

96.

Which of the following conclusions CANNOT be drawn just by looking at the diagram?

a)

GH and AB intersect at D

b)

<GDA and <HDB are vertical angles

c)

D is the midpoint of GH

d)

G, D, and H are collinear

97.
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
98.
What is the reason?
a)
Definition of Complementary
b)
Definition of supplementary
99.
What is the reason?
a)
Definition of congruence
b)
Definition of Angle
100.
What is the reason?
a)
Definition of bisects
b)
Definition of Congruence
101.

How can you prove step #4?

a)

Vertical angle theorem

b)

Subtraction property of equality

c)

Transitive property of congruence

d)

Definition of supplementary angles

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