Practice A 1-3

Name
LESSON
1-3
Date
Class
Practice A
Measuring and Constructing Angles
Use the figure for Exercises 1– 4.
1. An angle is a figure formed by two rays with a common
vertex
endpoint called the
1
.
3
2. Name the two rays that form ⬔P.
___›
___›
0
PQ and PR
2
4
3. Use the angle symbol and three letters to name ⬔P in two ways.
⬔QPR and ⬔RPQ
4. Name a point that is in the interior of ⬔P.
point S
#
Complete the statement.
protractor
is called a
5. A tool used to measure and draw angles
.
7. ⬔AEB
90; right
"
%
$
Find the measure of each angle. Then tell whether
each is acute, right, obtuse, or straight.
6. ⬔CEA
!
8. ⬔DEA
60; acute
180; straight
Complete the angle.
9. Use a compass and straightedge to finish constructing ⬔IHJ congruent to ⬔MLN.
*
.
,
(
-
)
(
10. Marc doesn’t think that the angle of the front seat
in his mom’s car is very cool, so he tilts the seat
back. m⬔ZWY 95 and m⬔YWX 30.
Find m⬔ZWX.
)
9
8
125
7
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
19
:
Holt Geometry
Name
LESSON
1-3
Date
Class
Practice B
Measuring and Constructing Angles
Draw your answer on the figure.
1. Use a compass and straightedge
to
___›
construct angle bisector DG .
%
'
&
$
#
2. Name eight different angles in the figure.
⬔A, ⬔C, ⬔ABC, ⬔ABD, ⬔ADB,
"
⬔ADC, ⬔CBD, and ⬔CDB
$
!
9
8
Find the measure of each angle
and classify each as acute,
right, obtuse, or straight.
:
7
3. ⬔YWZ
4. ⬔XWZ
90; right
5. ⬔YWX
120; obtuse
30; acute
T is in the interior of ⬔PQR . Find each of the following.
6. m⬔PQT if m⬔PQR 25° and m⬔RQT 11.
14
7. m⬔PQR if m⬔PQR (10x 7), m⬔RQT 5x °, and m⬔PQT (4x 6).
123
__›
8. m⬔PQR if QT bisects ⬔PQR, m⬔RQT (10x 13), and m⬔PQT (6x 1).
9. Longitude is a measurement of position around the equator of
Earth. Longitude is measured in degrees, minutes, and seconds.
Each degree contains 60 minutes, and each minute contains
60 seconds. Minutes are indicated by the symbol and seconds
are indicated by the symbol . Williamsburg, VA, is located at
76°4225. Roanoke, VA, is located at 79°5730. Find the
difference of their longitudes in degrees, minutes, and seconds.
10. To convert minutes and seconds into decimal parts of a degree,
divide the number of minutes by 60 and the number of seconds
by 3,600. Then add the numbers together. Write the location of
Roanoke, VA, as a decimal to the nearest thousandths of a degree.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
20
44
31505
79.958
Holt Geometry
THINK AND DISCUSS
1. Explain why any two right angles are congruent.
___›
2. BD bisects ∠ABC. How are m∠ABC, m∠ABD, and m∠DBC related?
3. GET ORGANIZED Copy and
complete the graphic organizer.
In the cells sketch, measure,
and name an example of each
angle type.
1-3
��
��
��
��
��
��
��
Exercises
KEYWORD: MG7 1-3
KEYWORD: MG7 Parent
GUIDED PRACTICE
Vocabulary Apply the vocabulary from this lesson to answer each question.
1. ∠A is an acute angle. ∠O is an obtuse angle. ∠R is a
right angle. Put ∠A, ∠O, and ∠R in order from least
to greatest by measure.
2. Which point is the vertex of ∠BCD? Which rays form
the sides of ∠BCD?
SEE EXAMPLE
1
p. 20
SEE EXAMPLE
2
p. 21
�
�
�
�
3. Music Musicians use a metronome to keep time as
they play. The metronome’s needle swings back and
forth in a fixed amount of time. Name all of the
angles in the diagram.
Use the protractor to find the measure of each
angle. Then classify each as acute, right, or obtuse.
�
�
�
�
4. ∠VXW
5. ∠TXW
6. ∠RXU
�
�
�
�
�
SEE EXAMPLE
3
p. 22
L is in the interior of ∠JKM. Find each of
the following.
7. m∠JKM if m∠JKL = 42° and m∠LKM = 28°
8. m∠LKM if m∠JKL = 56.4° and m∠JKM = 82.5°
SEE EXAMPLE 4
p. 23
 bisects ∠ABC. Find each of the following.
Multi-Step BD
9. m∠ABD if m∠ABD = (6x + 4)° and m∠DBC = (8x - 4)°
10. m∠ABC if m∠ABD = (5y - 3)° and m∠DBC = (3y + 15)°
24
Chapter 1 Foundations for Geometry
PRACTICE AND PROBLEM SOLVING
Independent Practice
For
See
Exercises Example
11
12–14
15–16
17–18
1
2
3
4
Extra Practice
Skills Practice p. S4
Application Practice p. S28
11. Physics Pendulum clocks have been used since
1656 to keep time. The pendulum swings back
and forth once or twice per second. Name all of
the angles in the diagram.
�
��
�
Use the protractor to find the measure of each angle.
Then classify each as acute, right, or obtuse.
12. ∠CGE
13. ∠BGD
�
�
�
�
14. ∠AGB
�
T is in the interior of ∠RSU. Find each of
the following.
�
�
15. m∠RSU if m∠RST = 38° and
m∠TSU = 28.6°
�
�
16. m∠RST if m∠TSU = 46.7° and m∠RSU = 83.5°
 bisects ∠RST. Find each of the following.
Multi-Step SP
17. m∠RST if m∠RSP= (3x - 2)° and m∠PST = (9x - 26)°
18. m∠RSP if m∠RST = __52 y ° and m∠PST = (y + 5)°
Estimation Use the following information for Exercises 19–22.
Assume the corner of a sheet of paper is a right angle.
Use the corner to estimate the measure and classify
each angle in the diagram.
19. ∠BOA
20. ∠COA
21. ∠EOD
22. ∠EOB
�
�
�
�
��
Use a protractor to draw an angle with each of the following measures.
23. 33°
24. 142°
�
25. 90°
27. Surveying A surveyor at point S discovers
that the angle between peaks A and B is 3
times as large as the angle between peaks B
and C. The surveyor knows that ∠ASC is a
right angle. Find m∠ASB and m∠BSC.
�
26. 168°
�
�
�
�
28. Math History As far back as the 5th century B.C., mathematicians have been
fascinated by the problem of trisecting an angle. It is possible to construct an angle
with __14 the measure of a given angle. Explain how to do this.
Find the value of x.
29. m∠AOC = 7x - 2, m∠DOC = 2x + 8, m∠EOD = 27
30. m∠AOB = 4x - 2, m∠BOC = 5x + 10, m∠COD = 3x - 8
31. m∠AOB = 6x + 5, m∠BOC = 4x - 2, m∠AOC = 8x + 21
32. Multi-Step Q is in the interior of right ∠PRS. If m∠PRQ
is 4 times as large as m∠QRS, what is m∠PRQ?
�
�
�
�
�
�
1- 3 Measuring and Constructing Angles
25

Download Report