Name ____________________________________ Period ____ Date __________
G8 – Module 2,
Lesson 12
ESSENTIAL QUESTION:
How can algebraic concepts be applied to geometry?
8.G.A.5: Use informal arguments to establish facts about the angles created
when parallel lines are cut by a transversal.
Parallel lines, cut by a transversal...
Interior Angles
Alternate Interior Angles
Vertical
Using colored pencils, shade...
Exterior Angles
Alternate Exterior Angles
Corresponding Angles
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Name ____________________________________ Period ____ Date __________
Complementary Angles
Supplementary Angles
Definition in
words
Picture
Reminder(s)
Use the figure below to name each of the following angle pairs:
1
2
3
4
5
6
7
Angle
Angle
1
2
1
4
1
8
3
6
1
5
4
5
4
8
8
Name(s)
2
Name ____________________________________ Period ____ Date __________
The parallel lines may be drawn in any direction... it doesn't affect the angle relationships!
1
5
2
6
3
7
4
8
Classify each pair of angles as alternate interior, alternate exterior, or corresponding:
Angles 3 and 6
__________________________________________________________________
Angles 1 and 3
__________________________________________________________________
Angles 2 and 7
__________________________________________________________________
If the measure of Angle 6 is 150 degrees, then what is the measure of the following angles:
Angle 1 __________
Angle 2 __________ Angle 3 ________ Angle 4 __________
Angle 5 __________
Angle 6 __________ Angle 7 ________ Angle 8 __________
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Name ____________________________________ Period ____ Date __________
Complete the table with the appropriate angle measures:
What is the measure of the
COMPLEMENT?
Angle Measure
What is the measure of the
SUPPLEMENT?
30
45
90
110
Module 2 Lesson 12 VOCABULARY Practice
Line j is parallel
to
Use the diagram below to
fill in the blanks for #1-6.
a
c
e
g
line k and line
m is a
transversal.
m
f
b
d
j
k
h
4
Name ____________________________________ Period ____ Date __________
1)
 d and  h are ____________________ angles.  d
≅h
because a
≅d
because a
______________________ would map  d onto  h.
2)
 a and  d are ____________________ angles.  a
______________________ would map  a onto  d.
3)
 e and  d are _______________ _______________ angles.  e
≅d
because
a ___________________ followed by a __________________ would
map  e onto  d.
4)  b and  g are _______________ _______________ angles.  b
≅g
because
a ___________________ followed by a __________________ would
map  b onto  g.
5)  b and  c are ____________________ angles.  b
≅c
because a
______________________ would map  b onto  c.
6)  f and  c are _______________ _______________ angles.  f
≅c
because a
___________________ followed by a __________________ would map  f onto  c.
5
Name ____________________________________ Period ____ Date __________
Use the diagram below to
fill in the blanks for #7-11.
Line a is parallel
to line b and
line c is a
transversal.
a
2
1
4
3
b
7
6
8
5
c
7)
 6 and  8 are ____________________ angles.  ____ ≅  _____ because a
______________________ would ______  ____ onto  ____ .
8)
 2 and  7 are ____________________ angles.  ____ ≅  _____ because a
______________________ would ______  ____ onto  ____ .
6
Name ____________________________________ Period ____ Date __________
9)
 1 and  8 are _______________ _______________ angles.  ____ ≅  _____
because a ___________________ followed by a __________________
would ______  ____ onto  _____.
10)  6 and  4 are _______________ _______________ angles.  ____ ≅  _____
because a ___________________ followed by a __________________
would ______  ____ onto  _____.
11)  5 and  3 are ____________________ angles.  ____ ≅  _____ because a
______________________ would ______  ____ onto  ____ .
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Name ____________________________________ Period ____ Date __________
Lesson 12: Angles Associated with Parallel Lines
Lesson Summary
Angles that are on the same side of the transversal
in corresponding positions (above each of 𝐿1 and
𝐿2 or below each of 𝐿1 and 𝐿2 ) are called
corresponding angles. For example, ∠2 and ∠4 are
corresponding angles.
When angles are on opposite sides of the
transversal and between (inside) the lines 𝐿1 and
𝐿2 , they are called alternate interior angles. For
example, ∠3 and ∠7 are alternate interior angles.
When angles are on opposite sides of the
transversal and outside of the parallel lines (above
𝐿1 and below 𝐿2 ), they are called alternate exterior
angles. For example, ∠1 and ∠5 are alternate
exterior angles.
When parallel lines are cut by a transversal, any corresponding angles, any alternate interior angles, and any
alternate exterior angles are equal in measure. If the lines are not parallel, then the angles are not equal in
measure.
PROBLEM SET
Use the diagram below to answer problems 1–6, questions are on the next page.
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Name ____________________________________ Period ____ Date __________
From the diagram found on the bottom of pg. 8, answer the following:
1) Identify all pairs of corresponding angles.
Are the pairs of corresponding angles equal in measure?
How do you know?
2) Identify all pairs of alternate interior angles.
Are the pairs of alternate interior angles equal in measure?
How do you know?
3) Use an informal argument to describe why ∠1 and ∠8 are equal in measure if 𝐿1 ∥
𝐿2 .
4) Assuming 𝐿1 ∥ 𝐿2 if the measure of ∠4 is 73°, what is the measure of ∠8?
How do you know?
5) Assuming 𝐿1 ∥ 𝐿2 , if the measure of ∠3 is 107° degrees, what is the measure of ∠6?
How do you know?
6) Assuming 𝐿1 ∥ 𝐿2 , if the measure of ∠2 is 107°, what is the measure of ∠7?
How do you know?
7) Would your answers to Problems 4–6 be the same if you had not been informed that
𝐿1 ∥ 𝐿2 ? Why, or why not?
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Name ____________________________________ Period ____ Date __________
8) Use an informal argument to describe why ∠1 and ∠5 are equal in measure if 𝐿1 ∥
𝐿2 .
9) Use an informal argument to describe why ∠4 and ∠5 are equal in measure if 𝐿1 ∥
𝐿2 .
10) Assume that 𝐿1 is not parallel to 𝐿2 . Explain why ∠3 ≠ ∠7.
10