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UNIT 8 MIXED REVIEW
Assessment readiness
1. Determine whether each pair of
angles is a pair of vertical angles,
a linear pair of angles, or neither.
Select the correct answer for each
lettered part.
C
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D
B
E
F
A
A. ∠AFC and ∠CFD
Vertical
Vertical
Vertical
B. ∠AFB and ∠CFD
C. ∠BFD and ∠AFE
Linear Pair
Linear Pair
Linear Pair
Neither
Neither
Neither
2. Does each transformation map a triangle in Quadrant II to Quadrant I?
Select Yes or No for A–C.
Yes
No
A. A rotation of 270°
B. A translation along the vector (-2, -2)
Yes
No
C. A reflection across the y-axis
Yes
No
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3. Are the triangles necessarily congruent?
Select Yes or No for each statement.
D
75°
5.7 cm
A
42°
F
63°
6.2 cm
B
C
8.1 cm
A. AC = 5.7 cm
B. m∠BAC = 75°, m∠ABC = 63°, and DE = 6.2 cm
C. m∠ACB = 42°, m∠ABC = 63°, and FE = 8.2 cm
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Yes
Yes
Yes
No
No
No
E
4. Triangle △ABC is in the second quadrant and translated along ​(-3, 2)​and
reflected across the y-axis. Determine if the translation will be in the given
quadrant. Select Yes or No for each statement.
A. In the first quadrant after the
first transformation
Yes
No
B. In the second quadrant after the
first transformation
Yes
No
C. In the third quadrant after the
second transformation
Yes
No
_
_
​ , 
5. Given
△ABC where A​(2, 3)​, B​(5, 8_
)​, C​(8, 3_
)​, ​RS​ is the midsegment parallel to AC​
_
​ST​
 
is
the
midsegment
parallel
to
AB​
​
 
,
and
​
RT​
 
is
the
midsegment
parallel
to
​
_
BC​ 
, determine if the statements are true or false. Select True or False for each
statement.
_
A. ​ST​ = 4
True
False
_
B. ​RT​ = 5
True
False
_
C. ​RS​ = 3
True
False
6. Find each angle measure.
Y
X
68°
Z
128°
ℓ
m
Statements
Unit 8
Reasons
1182
t
1 2
3 4
5 6
7 8
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7. Write a proof in two-column form for the Corresponding Angles Theorem.
Given: ℓ∥m
Prove: m∠3 = m∠7​
Performance Tasks
8. An employee is walking home from work and wants to take the long way to get
more exercise. The diagram represents the two different routes, where A is the
employee’s work and B is the employee’s home. Which route is longer and by
how much? Show your work.
3.8 miles
A
2.1 miles
B
9. A student was given the following triangle and asked to find the circumcenter.
Find the point and explain the steps for finding it.
y
C
(6, 7)
6
4
A
(-1, 2)
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0
10. While constructing a roof, a construction company built a triangle frame
with a base 25 feet long. A cross bar needs to be inserted that connects
the midpoints of both sides of the frame. Draw an image to represent the
situation and then describe how much wood is needed for the crossbar.
Assume the triangle is isosceles. Explain your answer.
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B
(6, 2)
2
4
6
x
math in careers
Architect An architect is writing the blueprints for a large triangular building to go in the
middle of a city. The building needs to be congruent to a building that is already made, but
the blueprints for the previous building were lost. What information will need to be known
about each triangular face of the building in order to make sure all faces are congruent,
knowing the building does not have any right triangles? Explain each possibility using
known triangle congruence theorems and postulates.
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