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Transcript
```Name
LESSON
1-4
Date
Class
Practice B
Pairs of Angles
180
1. ⬔PQR and ⬔SQR form a linear pair. Find the sum of their measures.
___›
QR
2. Name the ray that ⬔PQR and ⬔SQR share.
Use the figures for Exercises 3 and 4.
137.9
3. supplement of ⬔Z
4. complement of ⬔Y
X :
(110 8x)
9
5. An angle measures 12 degrees less than three times its supplement. Find the
measure of the angle.
132
6. An angle is its own complement. Find the measure of a supplement to this angle.
135
7. ⬔DEF and ⬔FEG are complementary. m⬔DEF (3x 4)°, and m⬔FEG (5x 6)°.
Find the measures of both angles. m⬔DEF
29; m⬔FEG 61
8. ⬔DEF and ⬔FEG are supplementary. m⬔DEF (9x 1)°, and m⬔FEG (8x 9)°.
Find the measures of both angles. m⬔DEF
91; m⬔FEG 89
Use the figure for Exercises 9 and 10.
In 2004, several nickels were minted to commemorate the Louisiana
Purchase and Lewis and Clark’s expedition into the American West. One
nickel shows a pipe and a hatchet crossed to symbolize peace between
the American government and Native American tribes.
9. Name a pair of vertical angles.
Possible answers: ⬔1 and ⬔3
or ⬔2 and ⬔4
10. Name a linear pair of angles.
Possible answers: ⬔1 and ⬔2; ⬔2 and ⬔3; ⬔3 and ⬔4; or ⬔1 and ⬔4
11. ⬔ABC and ⬔CBD form a linear pair and have
equal measures. Tell if ⬔ABC is acute, right,
or obtuse.
right
__›
12. ⬔KLM and ⬔MLN are complementary. LM
bisects ⬔KLN. Find the measures of ⬔KLM
and ⬔MLN.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
28
45°; 45°
Holt Geometry
Name
LESSON
1-4
Date
Class
Name
Practice A
1-4
Complete the statements.
side
, but no common interior points.
Use the figures for Exercises 3 and 4.
90�
4. complement of �Y
.
5.
measure of the angle.
.
angles are two angles whose measures
Find the measures of both angles. m�DEF
��������������
Find the measures of both angles. m�DEF
9. Name a pair of vertical angles.
� �
Possible answers: �1 and �3
In an equilateral triangle, all three sides have equal lengths
and all three angles have equal measures. Find the measure
of the following angles.
9. supplement of �A
120�
30�
or �2 and �4
11. �ABC and �CBD form a linear pair and have
equal measures. Tell if �ABC is acute, right,
or obtuse.
��������������
27
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name
right
__›
12. �KLM and �MLN are complementary. LM
bisects �KLN. Find the measures of �KLM
and �MLN.
�
�
1-4
�
�
Possible answers: �1 and �2; �2 and �3; �3 and �4; or �1 and �4
���
Draw your answer in the space provided.
LESSON
�
�
10. Name a linear pair of angles.
�
11. Sketch �1 and �2 so that
they are vertical angles.
� 91�; m�FEG � 89�
Use the figure for Exercises 9 and 10.
In 2004, several nickels were minted to commemorate the Louisiana
Purchase and Lewis and Clark’s expedition into the American West. One
nickel shows a pipe and a hatchet crossed to symbolize peace between
the American government and Native American tribes.
�
��������������
10. complement of �A
� 29�; m�FEG � 61�
8. �DEF and �FEG are supplementary. m�DEF � (9x � 1)°, and m�FEG � (8x � 9)°.
�
8. Sketch �1 and �2 so that
they form a linear pair.
132�
7. �DEF and �FEG are complementary. m�DEF � (3x � 4)°, and m�FEG � (5x � 6)°.
.
Draw your answer in the space provided.
7. Sketch �1 and �2 so that
they are adjacent angles.
�����
135�
6. The kind of angle formed by the noncommon sides of two adjacent and
straight angle
�
6. An angle is its own complement. Find the measure of a supplement to this angle.
have a sum of 180�.
supplementary angles is a
(110 � 8x)�
5. An angle measures 12 degrees less than three times its supplement. Find the
4. The kind of angle formed by the noncommon sides of two adjacent and
Supplementary
Date
Holt Geometry
Class
Name
LESSON
1-4
Pairs of Angles
Draw your answers in the space provided.
1. Draw two intersecting lines and label the resulting
angles with the numbers 1, 2, 3, and 4.
2. Label �1 with x �. �1 and �2 are supplementary.
Find the measure of �2 and label the diagram.
45°; 45°
28
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Practice C
Date
Pairs of Angles
Angle Pairs
��������������
�������� ��
�
�� �
� ��
�
Adjacent Angles
have the same vertex and
share a common side
Linear Pairs
adjacent angles whose
noncommon sides are
opposite rays
Vertical Angles
nonadjacent angles formed
by two intersecting lines
3. �3 is also supplementary to �2. Find the measure of �3 and label the diagram.
�
�
�
�
The measures of the vertical angles are equal.
�1 and �2 are adjacent.
5. �X is complementary to �Y, and �Z is also complementary to �Y.
Explain why �X and �Z are congruent.
�
�
�3 and �4 are adjacent
and form a linear pair.
�5 and �6 are vertical
angles.
Tell whether �7 and �8 in each figure are only adjacent, are adjacent and form a
linear pair, or are not adjacent.
If m�X � m�Y � 90� and m�Z � m�Y � 90�, then m�X and m�Z
2.
1.
are both equal to 90� � m�Y. So m�X � m�Z. Two angles whose
�
�
measures are equal are congruent.
Adjacent angles are defined as two angles in the same plane with a common
vertex and a common side, but no common interior points.
3.
�
adjacent and form
a linear pair
6. �ADB and �CDB are adjacent angles. If the phrase “but no common interior
points” was not part of the definition, name another pair of angles that would
qualify as adjacent.
�
�
only adjacent
not adjacent
only adjacent
4. �5 and �4
�
�
Draw your answer in the space provided.
7. Draw a diagram that shows why the
definition of adjacent angles includes
the phrase “in the same plane.”
Use the figure for Exercises 8 –10.
9. �3 is a right angle
60�
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
45�
29
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
5. �1 and �4
not adjacent
6. �2 and �3
adjacent and form a linear pair
Name each of the following.
7. a pair of vertical angles
�
�
�
Tell whether the indicated angles are only adjacent, are adjacent and
form a linear pair, or are not adjacent.
Possible answer: �ADB and �ADC
This diagram shows a ray of light reflecting off a mirror.
When light reflects, the incident angle and the reflected
angle are congruent, that is, �1 � �2. Find the measure
of �1 in each situation below.
Holt Geometry
Class
Reteach
4. From your work in Exercises 1–3, make a conclusion about the measures
of the vertical angles.
8. �1 � �3
�
����������
137.9�
3. supplement of �Z
3. Complementary angles are two angles whose measures have a sum of
right angle
180�
___›
QR
2. Name the ray that �PQR and �SQR share.
2. A linear pair is a pair of adjacent angles whose noncommon sides
are opposite rays.
complementary angles is a
Pairs of Angles
1. �PQR and �SQR form a linear pair. Find the sum of their measures.
vertex
1. Adjacent angles are two angles in the same plane with a common
Class
Practice B
LESSON
Pairs of Angles
and a common
Date
�
10. m�1 � 2m�3
8. a linear pair
�
Possible answers:
�1 and �6, �2 and �5
Possible answers: �1 and �2;
�1 and �5; �5 and �6; �6 and �2
�
72�
9. an angle adjacent to �4
Holt Geometry
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
65
�
�
�
�
�
� �
�3
30
Holt Geometry
Holt Geometry
```
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