Download Understand Angle Relationships Vocabulary

Lesson 21
Understand
Angle Relationships
Name: Prerequisite: How can you use facts about angles
to help you find a missing angle measure?
Study the example showing how to find the measure of
a missing angle. Then solve problems 1–6.
Example
Triangle ABC is a right triangle whose right angle is  ABC.
Find the measure of EBF.
 ABC and  DBF are vertical angles, so they have the same
measure. Because m ABC is 90°, the sum of m DBE and
m EBF must also be 90°.
Solve for x in this equation.
D
(x 2 12)8
E
A
B
x8
F
G
x 1 (x 2 12) 5 90
2x 2 12 5 90
C
2x 5 102
x 5 51
m EBF 5 51°
1 What is m DBE? Explain.
2 What is m GBC? Explain.
3 Explain how to find m ABD.
Vocabulary
complementary angles two angles whose
measures add to 90°.
supplementary angles two angles whose
measures add to 180°.
vertical angles the non-adjacent angles
formed by intersecting
lines. Vertical angles
have the same measure.
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Lesson 21 Understand Angle Relationships
219
Solve.
l
l
4 In the diagram, EA ​
​   ' ​ 
  EC ​
,  and BD is a straight line.
 
 
·
·
B
Find the value of x.
Show your work.
E
(3x 2 10)8
x8
A
C
D
Solution: Use the diagram at the right to solve problems 5–6.
5 Explain how you would find m STQ.
N
M
S
(2x 1 8
)8
(71 2 x)8
T
P
Q
6 Find m STQ.
Show your work.
Solution: 220
Lesson 21 Understand Angle Relationships
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Lesson 21
Name: Identify Angle Pairs
Study the example showing how to use angle pair
relationships to find measures of angles. Then solve
problems 1–5.
Example
In the diagram, lines w, x, and y are parallel. Use the
terms corresponding angles, alternate interior angles,
and linear pair to describe some of the angle
relationships in the diagram.
w
x
1 3
2
4
1 and 9 are corresponding angles.
Corresponding angles formed by a transversal
crossing parallel lines are congruent, so 1 > 9.
5 7
6
8
y
9
11
10
12
 4 and  5 are alternate interior angles. Alternate interior
angles between parallel lines are congruent, so  4 >  5.
1 and 3 form a linear pair. Linear pairs are supplementary,
so m1 1 m 3 5 180°.
1 Use the diagram in the example. Name a different pair
of corresponding angles, a different pair of alternate
interior angles, and a different linear pair.
corresponding angles: alternate interior angles: linear pair: 2 Use the diagram in the example. If m7 5 108°, what is
m12? Explain how you found the measure.
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Vocabulary
transversal a line that
crosses two lines.
corresponding
angles angles in the
same position in the
intersections of a
transversal and two or
more parallel lines.
alternate interior
angles angles between
two parallel lines and on
opposite sides of a
transversal.
linear pair adjacent
supplementary angles.
Lesson 21 Understand Angle Relationships
221
Solve.
Use the diagram shown to solve problems 3–5.
3 In the diagram, lines a and b are parallel, with
m 3 5 65° and m11 5 100°. Find the measures of
 2,  5, and 13. Tell which angle relationships you used
to help you find each measure.
m 2: d
c
1 2
4 3
a
b
13 14
16 15
5 6
8 7
9 10
12 11
m 5: m13: 4 Find the measures of angles 3, 8, 9, and 14 to show that
the sum of the interior angles of a trapezoid is 360°. Tell
which angle relationships you used.
Show your work.
Solution: 5 Are  3 and  5 congruent? Explain.
222
Lesson 21 Understand Angle Relationships
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Lesson 21
Name: Reason and Write
Study the example. Underline two parts that you think
make it a particularly good answer and a helpful example.
Example
Elena drew a map of a neighborhood park. She says that the
park has three straight sidewalks, two of which are parallel.
Her map shows vertical angles, corresponding angles,
alternate interior angles, and linear pairs of angles that are
formed by the three straight sidewalks in the park.
Draw a map of a park that matches Elena’s description. Label
the sidewalks m, n, and p, and label the angles formed by the
sidewalks 1, 2, 3, 4, and so on.
Describe how the lines for the sidewalks are related. Name
one pair of angles in your map to illustrate each angle
relationship mentioned in Elena’s description. Tell how you
know that the angles illustrate the relationship.
Show your work. Use a diagram,
words, and angle relationships to
explain your answer.
Possible answer:
m
Where does the
example . . .
n
1 2
4 3
• answer each part
of the problem?
5 6
8 7
p
• use a diagram to
illustrate?
• use words to
explain?
Lines m and n are parallel, and line p is a transversal that
intersects the two parallel lines.
• use angle
relationships to
explain?
/1 and /3 are vertical angles because they are
non-adjacent angles formed by intersecting lines.
/1 and /5 are corresponding angles because they are in the same
position in the intersections of the transversal and the parallel lines.
/2 and /8 are alternate interior angles because they are between
two parallel lines and on opposite sides of the transversal.
/1 and /2 form a linear pair because they are adjacent
supplementary angles.
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Lesson 21 Understand Angle Relationships
223
Solve the problem. Use what you learned from the model.
Von makes a design with four lines. At least two of them are
parallel. He says that his design shows vertical angles,
corresponding angles, alternate interior angles, and linear
pairs of angles.
Draw a diagram of Von’s design. Label the lines a, b, c, and d,
and label the angles formed by the lines 1, 2, 3, 4, and so on.
Describe how the lines are related. List all of the angles that
are congruent to 1 in your diagram. Then list all of the
angles that are congruent to  2.
Name one pair of angles in your diagram to illustrate each
angle relationship mentioned in Von’s description. Tell how
you know that the angles illustrate the relationship.
Show your work. Use a diagram, words, and angle
relationships to explain your answer.
Did you . . .
• answer each part
of the problem?
• use a diagram to
illustrate?
• use words to
explain?
• use angle
relationships to
explain?
224
Lesson 21 Understand Angle Relationships
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