10-6
10-6
Circles and Arcs
1. Plan
Objectives
1
2
To find the measures of
central angles and arcs
To find circumference and
arc length
Examples
1
2
3
4
5
Real-World Connection
Identifying Arcs
Finding the Measures of Arcs
Real-World Connection
Finding Arc Length
What You’ll Learn
Check Skills You’ll Need
• To find the measures of
GO for Help Lesson 1-9 and Skills Handbook, p. 761
Find the diameter or radius of each circle.
central angles and arcs
• To find circumference and
arc length
1. r = 7 cm, d = 7 14 cm
2. r = 1.6 m, d = 7 3.2 m
3. d = 10 ft, r = 7 5 ft
4. d = 5 in., r = 7 2.5 in.
. . . And Why
Round to the nearest whole number.
To use the turning radius of a
car to compare the distances
that its tires travel, as in
Example 4
5. 9% of 360 32
6. 38% of 360 137
7. 50% of 360 180 8. 21% of 360
76
New Vocabulary • circle • center • radius • congruent circles
• diameter • central angle • semicircle • minor arc
• major arc • adjacent arcs • circumference • pi
• concentric circles • arc length • congruent arcs
Math Background
The ratio p of a circle’s
circumference to its diameter
is independent of the size of
the circle (C = pd). Ancient
calculations of p range from the
rather crude 3 to a remarkably
accurate 355
113 . In 1999, a computer
calculated the constant p to
206,158,430,000 decimal places.
Results such as this are used to
check the accuracy of other
computer programs.
1
Central Angles and Arcs
In a plane, a circle is the set of all points equidistant from
a given point called the center. You name a circle by its
center. Circle P (P) is shown at the right.
Vocabulary Tip
Diameter comes from the
classical Greek words dia,
meaning through, and
meter, meaning measure.
A
P
B
A radius is a segment that has one endpoint at the
center and the other endpoint on the circle. PC is a
radius. PA and PB are also radii. Congruent circles
have congruent radii.
A diameter is a segment that contains the center of a
circle and has both endpoints on the circle. AB is a diameter.
More Math Background: p. 530D
A central angle is an angle whose vertex is the center of the circle. &CPA is a
central angle.
Lesson Planning and
Resources
1
See p. 530E for a list of the
resources that support this lesson.
PowerPoint
Bell Ringer Practice
Check Skills You’ll Need
For intervention, direct students to:
6
4
/
.
8
.
.
.
.
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
/
Finding Circumference
EXAMPLE
Real-World
Connection
Gridded Response To learn how people really spend
their time, a research firm studied the hour-by-hour
activities of 3600 people. The participants were
between 18 and 90 years old. Each participant was
sent a 24-hour recording sheet every March for
three years from 2000 to 2002.
Some information from the study is shown in this
circle graph. What is the measure, in degrees, of the
central angle used for the Entertainment part?
Sleep
Other
15%
31%
ADMIT
ONE
Entertainment
18%
9% 20% 7%
Must
Do
Food
Work
There are 360 degrees in a circle. To find the measure of a
central angle in the circle graph, find the corresponding percent of 360.
Entertainment is 18%, and 18% of 360 = 0.18 ? 360, or 64.8.
Lesson 1-9: Example 2
Extra Skills, Word Problems, Proof
Practice, Ch. 1
Finding Percentages of a Number
C
566
Chapter 10 Area
Skills Handbook, p. 761
Special Needs
Below Level
L1
Make sure students understand that p is a constant
and not a variable. Also, show them how they can
estimate the circumference of a circle by
approximating 2pr or pd with 6 r or 3 d.
566
learning style: verbal
L2
Students may use objects such as aluminum cans and
pieces of string to help them understand the formula
for the circumference of a circle.
learning style: tactile
2. Teach
You can use the same method to find the measures of the other central angles.
Sleep: 31% of 360 = 111.6
Other:
15% of 360 = 54
Food: 9% of 360 = 32.4
Must Do:
7% of 360 = 25.2
Guided Instruction
Work: 20% of 360 = 72
Quick Check
B
A
1
4
5
A
A
B
B
E
D
E
D
C
B
E
D
C
B
A
3
C
B
A
2
E
D
C
C
C
1 a. Critical Thinking Each section of the circle graph represents a measurable
quantity. What is that quantity? number of hours spent doing an activity
b. Each section of the circle graph represents an average. Explain.
Each section represents the average of the 3000± participants’ answers.
D
D
E
E
Test-Taking Tip
An arc is a part of a circle. One type of arc, a semicircle, is half of a circle.
A minor arc is smaller than a semicircle. A major arc is greater than
a semicircle.
You can also find the
measure a of a central
angle by using a
proportion. For
Entertainment (18%) in
R
18 5 a .
Example 1: 100
360
T
R
S
P
T
TRS is a semicircle.
mTRS 180
R
S
P
S
P
T
RS is a minor arc.
mRS mRPS
RTS is a major arc.
mRTS 360 mRS
EXAMPLE
Careers
EXAMPLE
Because two points name two
arcs on a circle, naming an arc
using just two points can cause
confusion. Point out that this
book uses two points to name
minor arcs and three points to
name semicircles and major arcs.
Teaching Tip
Identifying Arcs
Identify the following in O.
A
a. the minor arcs
000
0
AD , CE , AC , and DE are minor arcs.
The water line separates a
circle into a major arc and a
minor arc.
EXAMPLE
Statisticians are applied
mathematicians. Most public
and private companies hire
statisticians to gather and
analyze data using mathematical
techniques. Colleges offer
programs to prepare students
for careers as statisticians.
2
The measure of a semicircle is 180. The measure of a minor arc is the measure of its
corresponding central angle. The measure of a major arc is 360 minus the measure
of its related minor arc.
2
1
When you introduce adjacent
arcs, ask: If two arcs are adjacent,
are their corresponding central
angles adjacent? yes What do
adjacent angles have in common?
one side
C
O
D
E
b. the semicircles
1 1 1
1
ACE , CED , EDA , and DAC are semicircles.
c. the major arcs that contain point A
11 1
1
ACD, CEA , EDC, and DAE are major arcs that contain point A.
Quick Check
2 Identify the four major arcs of O that contain point E.
1 1 1 1
CEA , DAE , ACD , EDC
Adjacent arcs are arcs of the same circle that have exactly one point in common.
You can add the measures of adjacent arcs just as you can add the measures of
adjacent angles.
Key Concepts
Postulate 10-1
Arc Addition Postulate
The measure of the arc formed by two adjacent
arcs is the sum of the measures of the two arcs.
1
0
0
mABC = mAB + mBC
C
B
A
Lesson 10-6 Circles and Arcs
Advanced Learners
567
English Language Learners ELL
L4
After Example 4, ask students to calculate which is
greater, the height or the circumference of a can of
three tennis balls.
learning style: verbal
Some students may confuse the term circumference
with the term circumscribe. Emphasize that
circumference is “the length around a circle” and
circumscribe is a verb meaning “to draw around.”
learning style: verbal
567
3
Math Tip
EXAMPLE
3
Relate the Arc Addition Postulate
to the Angle Addition Postulate
in Lesson 1-6.
EXAMPLE
Finding the Measures of Arcs
Find the measure of each arc.
0
0
a. BC
mBC = m&BOC = 32
0
0
0
0
BD = mBC + mCD
b. BD
m0
mBD = 32 + 58 = 90
1
1
c. ABC
ABC
1is a semicircle.
mABC = 180
0
0
d. AB
mAB = 180 - 32 = 148
PowerPoint
Additional Examples
1 A researcher surveyed 2000
members of a club to find their
ages. The graph shows the survey
results. Find the measure of each
central angle in the circle graph.
Quick Check
58
C
B 32
D
O
A
1 0
1
3 Find m&COD, mCDA , mAD and mBAD . 58; 180; 122; 270
Members’ Ages
2
1
Circumference and Arc Length
25%
40%
The circumference of a circle is the distance around the circle. The number pi (p)
is the ratio of the circumference of a circle to its diameter.
8%
27%
65
4564
Key Concepts
2544
Under 25
Theorem 10-9
Circumference of a Circle
The circumference of a circle is p times the diameter.
65±: 90; 45–64: 144;
25–44: 97.2; Under 25: 28.8
d
C = pd or C = 2pr
C
2 Identify the minor arcs, major
arcs, and semicircles in P with
point A as an endpoint.
Since the number p is irrational, you cannot write it as a terminating or repeating
decimal. To approximate p, you can use 3.14, 22
key on your calculator.
7 , or the
D
A
r
O
Circles that lie in the same plane and have the same center are concentric circles.
P
B
4
E
0 0
minor arcs:1
;
AD , AE
1
major arcs: 1
ADE , 1
AED ;
semicircles: ADB , AEB
0
1
3 Find m XY and mDXM in C.
EXAMPLE
Real-World
Connection
Automobiles A car has a turning radius of 16.1 ft. The distance between the two
front tires is 4.7 ft. In completing the (outer) turning circle, how much farther does
a tire travel than a tire on the concentric inner circle?
To find the radius of the inner circle, subtract 4.7 ft from the turning radius.
16.1 ft
M
circumference of outer circle = C = 2pr = 2p(16.1) = 32.2p
radius of the inner circle = 16.1 - 4.7 = 11.4
Y
40°
D
4.7 ft
56°
C
W
The difference in the two distances is 32.2p - 22.8p, or 9.4p.
9.4p <
X
29 . 53 09 7 1
Use a calculator.
A tire on the turning circle travels about 29.5 ft farther than a tire on the
inner circle.
0
1
m XY ≠ 96; mDXM ≠ 236
Quick Check
568
568
circumference of inner circle = C = 2pr = 2p(11.4) = 22.8p
Chapter 10 Area
4 The diameter of a bicycle wheel is 22 in. To the nearest whole number, how many
revolutions does the wheel make when the bicycle travels 100 ft?
17 revolutions
The measure of an arc is in degrees while the arc length is a fraction of a circle’s
60
circumference. An arc of 608 represents 360
or 16 of the circle. Its arc length is 16 the
circumference of the circle. This observation suggests the following theorem.
Key Concepts
Theorem 10-10
A
5
EXAMPLE
r
O
B
P
0
length of XY
0
= mXY
360 ? pd
0
90 ? p(16)
length of XY = 360
= 4p in.
Quick Check
60
60
EXERCISES
O
Error Prevention!
Y
1
length of XPY
240
1
= mXPY
360 ? 2pr
1
length of XPY = 240
360 ? 2p(15)
= 20p cm
5 Find the length of a semicircle with radius 1.3 m. Leave your answer in terms of p.
1.3π m
It is possible for two arcs of different circles to have the same measure but different
lengths, as shown at the left. It is also possible for two arcs of different circles to
have the same length but different measures. Congruent arcs are arcs that have
the same measure and are in the same circle or in congruent circles.
For more exercises, see Extra Skill, Word Problem, and Proof Practice.
Some students may confuse arc
length with the measure of an
arc. Point out that arc length is
often given in terms of p, unlike
the measure of an arc.
PowerPoint
Additional Examples
4 A circular swimming pool with
a 16-ft diameter will be enclosed
in a circular fence 4 ft from the
pool. What length of fencing
material is needed? Round to the
nearest whole number. 75 ft
1
5 Find the length of A D B in M
in terms of p.
B
Practice and Problem Solving
A
Practice by Example
Example 1
GO for
Help
(page 566)
Trash The graph shows types of trash
in a typical American city. Find the
measure of each central angle to the
nearest whole number.
1. Glass 18
2. Metals 29
3. Plastics 40
4. Wood 22
43 5. Food Waste
7. Other
40
6. Yard Waste 43
8. Paper and Paperboard
126
Connection to
Engineering
Point out that, although p is a
symbol, it is a constant, not a
variable.
15 cm
Y
EXAMPLE
Connection to Algebra
Finding Arc Length
Find the length of each arc shown in red. Leave your answer in terms of p.
a.
b.
X
X
O
16 in.
4
Ask: If the left wheels travel a
different distance from the right
wheels in the same amount of
time, what can you conclude
about their speeds? The left
wheels spin faster than the right
wheels. The car’s differential
enables the wheels to do this.
Arc Length
The length of an arc of a circle is the product of the ratio
measure of the arc and the circumference of the circle.
360
0
0
length of AB = mAB
? 2pr
360
Guided Instruction
Yard
Waste
12%
Other 11%
Paper and
Paperboard
35%
A
D
21π cm
Food
Waste
12%
Glass
5%
Plastics 11% Metals 8%
150° 18 cm
M
Resources
• Daily Notetaking Guide 10-6
Wood
6%
L3
• Daily Notetaking Guide 10-6—
L1
Adapted Instruction
SOURCE: Environmental Protection Agency, 2003.
Go to www.PHSchool.com for a data update.
Web Code: aug-9041
Lesson 10-6 Circles and Arcs
569
Closure
One section of a circle graph
with a radius of 15 in. is labeled
“Radio: 20%.” Find the measure
and length of the arc corresponding to this section of the
circle graph. measure: 72;
569
3. Practice
Example 2
(page 567)
Assignment Guide
1 A B 1-26, 40-53
Example 3
2 A B
27-39, 54-69
C Challenge
70-72
Test Prep
Mixed Review
(page 568)
73-75
76-83
Example 4
Homework Quick Check
(page 568)
To check students’ understanding
of key skills and concepts, go over
Exercises 8, 37, 59, 62, 67.
9–14. Answers may vary.
Identify the following in O. Samples are given.
F
1
0
9. a minor arc ED
10. a major arc FEB
O
B
1
E
11. a semicircle BFE
12. a pair of adjacent
0arcs 0
FE and ED
D
C
13. an acute central angle 14. a pair of congruent angles
lFOE
lFOE and lBOC
Find the measure of each arc in P.
C
1
1
1
0
T
128
15. TC 128 16. TBD 180 17. BTC 218 18. TCB 270
0
1
1
0
P
D
19. CD 52
20. CBD 308 21. TCD 180 22. DB 90
1
1
0
0
B
23. TDC 232 24. TB 90
25. BC 142 26. BCD 270
Find the circumference of each circle. Leave your answer in terms of π.
27.
28.
20π cm
O
20 cm
6π ft
29.
πm
32.
3 ft
4.2 m
8.4π m
Exercise 14 Have students explain
why the two angles are congruent.
30.
31.
14π in.
14 in.
Error Prevention!
1
m
2
Exercises 15–26 Remind students
that this textbook names minor
arcs with two points and semicircles
and major arcs with three points.
Exercise 40 Challenge students to
construct a central angle on A
and construct a congruent central
angle on B.
Example 5
(page 569)
33. The wheel of an adult’s bicycle has diameter 26 in. The wheel of a child’s
bicycle has diameter 18 in. To the nearest inch, how much farther does the
larger bicycle wheel travel in one revolution than the smaller bicycle wheel?
25 in.
Find the length of each arc shown in red. Leave your answer in terms of π.
34.
35.
14 cm
8π ft
cm
38.
33π in.
L3
B
L2
Apply Your Skills
L1
Adapted Practice
Practice
Name
Class
L3
Date
Practice 10-6
Volumes of Pyramids and Cones
Find the volume of each pyramid.
54 cm
1.
2.
3.
at McClellan High School
32 in.
32 in.
34 in.
45 cm
10 in.
10 in.
4.
5.
GO
6.
150 m2
18 cm
36 yd
400 yd 2
3m
Find the volume of each cone. Round your answers to the nearest tenth.
8.
9.
24 cm
Homework Help
Visit: PHSchool.com
Web Code: aue-1006
8 cm2
7.
nline
28 m
26 m
12 in.
© Pearson Education, Inc. All rights reserved.
10 cm
10 in.
10.
8 in.
11.
12.
2 ft
15 m
17 m
13 in.
6 ft
Algebra Find the value of the variable in each figure.
13.
14.
x
15.
14
x
6
15
15
Volume 1500
570
9
Volume 8π
x
Volume 126
570
Chapter 10 Area
25
9m
23π
2
O
m
5π
4
m
40. Use a compass
Then use
0 to draw A
0and B with different
0 radii.0
0a protractor
0
to draw XY on A and ZW on B so that mXY = mZW. Is XY > ZW ?
See margin, p. 571.
See margin,
41. Surveys Use the data in the table to construct a circle graph.
p. 571.
Interest in Languages by Students
13 in.
54 cm
27π m
39.
23 m
36 in.
L4
18 m
t
30
Reteaching
60
24 f
37.
Enrichment
36.
45
7π
2
GPS Guided Problem Solving
58π cm
29 cm
German
Japanese
Chinese
French
Spanish
24%
13%
12%
25%
26%
Error Prevention!
Find each indicated measure for O.
1
42. m&EOF 70
43. mEJH 180
1
45. m&FOG 55
46. mJEG 235
E
0
44. mFH 110
1
47. mHFJ 290
F
48. Open-Ended Make a circle graph showing how you
spend a 24-hour weekday. Check students’ work.
J
O
Exercise 57 Some students may
incorrectly use 200 ft as the radius
instead of the diameter.
70
H
Math Tip
G
Exercise 58 Suggest that students
Time Hands of a clock suggest an angle whose measure is continually changing.
49. Through how many degrees does a minute hand move in each time interval?
a. 1 minute 6
b. 5 minutes 30
c. 20 minutes 120
50. Through how many degrees does an hour hand move in each time interval?
a. 1 minute 0.5
b. 5 minutes 2.5
c. 20 minutes 10
51. What is the measure of the angle formed by the hands of a clock at 7:20? 100
x 2 Algebra Find the value of each variable.
P
R
A
c
Q (4c 10)
Real-World
Connection
In 5 minutes, the tip of the
minute hand of Boston’s
Custom House Tower
travels 6 ft 10 in.
38
means arc length here.
Exercise 70 Ask: Do the arcs in
part a have the same length?
Explain. No; the circles have
different radii.
(3x + 20)
A
(2x + 60)
Q
The circumference of a circle is 100π in. Find each of the following.
Connection to Sports
54. the diameter 100 in.
Exercise 72 Ask: Why might a
runner prefer to run on the inner
part of the track rather than the
outer? Sample: The distance
is less.
56. the length of an arc of 1208
55. the radius 50 in.
in.
on
ep
N
100π
3
e.
se
1
Rt
t.
tS
East St.
.
St
le
ap
n
ai
40
M
M
.
St
57. Multiple Choice Five streets come together at
a traffic circle. The diameter of the circle is
200 ft. If traffic travels counterclockwise, what
is the approximate distance from East St.
to Neponset St.? B
227 ft
244 ft
454 ft
488 ft
Problem Solving Hint
For Exercise 58, draw
A and B concentric.
Draw 608 and 458
angles that share a
side. To have equal arc
lengths, which circle
must be larger?
Exercise 61 Remind students to
use the Midpoint Formula.
Exercise 69 Point out that length
40
P
53. (x + 40)
52.
pick a whole-number value for the
radius of one circle and then find
r for the other circle. Point out
that the strategy stepping back
from abstract to concrete is often
a good way to begin solving.
40.
Z
58. A 608 arc of A has the same length as a 458 arc of B. Find the ratio of the
radius of A to the radius of B. 3 : 4
59. Metalworking Nina designed an arch
made of wrought iron for the top of
a mall entrance. The 11 segments
GPS
between the two concentric
semicircles are each 3 ft long. Find
the total length of wrought iron
used to make this structure. Round
your answer to the nearest foot. 105 ft
X
Y
W
A
B
no
41.
Japanese
13%
20 ft
German
24%
Chinese
12%
60. History In Exercise 31 on page 133, you learned that in 220 B.C., Eratosthenes
estimated the circumference of Earth. He did so by finding that on a great
circle of Earth, an arc of approximately 500 mi has a central angle of 7.28.
25,000 mi a. Use Eratosthenes’s measurements to estimate the circumference of Earth.
b. Compare your answer in part (a) to the actual circumference of Earth (at
the equator) of 24,902 mi. The estimate seems quite accurate.
Lesson 10-6 Circles and Arcs
Interest in Languages
French
25%
Spanish
26%
571
571
4. Assess & Reteach
PowerPoint
Lesson Quiz
Coordinate Geometry A diameter of a circle has endpoints A(1, 3) and B(4, 7).
Find each of the following.
GO for Help
The Distance and Midpoint
Formulas are on pages 53
and 55.
61. the coordinates of the center (2.5, 5)
Find the length of each arc shown in red. Leave your answer in terms of π.
63.
1. A circle graph has a section
marked “Potatoes: 28%.”
What is the measure of the
central angle of this section?
100.8
62. the circumference 5π units
64.
4.1 ft
50
65.
7.2 in.
6m
45
5.125π ft
2. Explain how a major arc differs
from a minor arc. A major arc
is greater than a semicircle.
A minor arc is smaller than
a semicircle.
2.6π in.
3π m
Use what you learn from Calvin’s father to answer Exercises 66 and 67.
Use O for Exercises 3–6.
S
W
Y
27 in.
60° O
X
0
3. Find mYW . 30
1
4. Find mWXS . 270
5. Suppose that P has a
diameter 2 in. greater than the
diameter of O. How much
greater is its circumference?
Leave your answer in terms
of p. 2π in.2
0
6. Find the length of XY . Leave
your answer in terms of p.
9π in.2
66. In one revolution, how much farther does a point 10 cm from the center of the
record travel than a point 3 cm from the center? Round your answer to the
nearest tenth. 44.0 cm
67. Outside; a point on
the outside travels
farther in the same
time, so it goes faster.
0
0
68. In O, the length of AB is 6p cm and mAB is 120. What is the diameter of
O? 18 cm
69. Coordinate Geometry Find the length of a semicircle with endpoints
(3, 7) and (3, -1). Round your answer to the nearest tenth. 12.6 units
Alternative Assessment
Provide each student with a
circle graph from a magazine
or newspaper. Have students
calculate the measures of the arcs,
circumferences of the circles, and
arc lengths to demonstrate how
the Arc Addition Postulate,
Circumference of a Circle Theorem,
and Arc Length Theorem apply to
their circle graphs.
67. Writing Kendra and her mother plan to ride the carousel. Two horses on the
carousel are side by side. For a more exciting ride, should Kendra sit on the
inside or the outside? Explain your reasoning. See left.
C
Challenge
70a. Answers0
may vary.
0
Sample: BD and FE
70. The two circles shown below
are concentric.
a. Name two arcs that have the
same measure.
b. Find the value of x. 35
F
B
71. Find the perimeter of the
shaded portion of the figure
below. Leave your answer in
terms of p. Explain your
reasoning and state what
assumptions you make.
2π in.; assumptions may vary.
70
x
G
x
A
O
D
4 in.
E
4 in.
572
572
Chapter 10 Area
Real-World
Connection
The track is longer for runners
on the outside, so the start of
the race is staggered.
72. Sports An athletic field is a rectangle, 100 yd by 40 yd, with a semicircle at each
of the short sides. A running track 10 yd wide surrounds the field. If the track is
divided into eight lanes of equal width, find the distance around the track along
the inside edge of each lane.
325.7 yd
333.5 yd
10 yd
341.4 yd
349.2 yd
100 yd
357.1 yd
40 yd
365.0 yd
372.8 yd
380.6 yd
Test Prep
Resources
For additional practice with a
variety of test item formats:
• Standardized Test Prep, p. 593
• Test-Taking Strategies, p. 588
• Test-Taking Strategies with
Transparencies
Test Prep
Multiple Choice
73. The radius of a circle is 12 cm. What is the length of a 60° arc? B
A. 3p cm
B. 4p cm
C. 5p cm
D. 6p cm
74. A 240° arc has length 16π ft. What is the radius of the circle? G
F. 6 ft
G. 12 ft
H. 15 ft
J. 24 ft
Short Response
75. Amy is constructing a curved path
through a rectangular yard. She
will edge the two sides of the
curved path with plastic edging.
Find the total length, in meters, of
plastic edging she will need.
Show your work or explain how
you found the total. See margin.
4m
2m
4m
[1] no work shown
79. No; it could be an
isosc. trap.
4m
2m
4m
80. Yes; if the diagonals
bisect each other, it is a
.
Mixed Review
GO for
Help
Lesson 10-5
75. [2] 21(2π? 6) ± 12(2π ? 4) ≠
6π ± 4π ≠ 10π;
10π m or about
31.4 m
Part of a regular 12-gon is shown at the right.
3
81. Yes; if one pair of sides
is both O and n, it is a .
4
76. Find the measure of each numbered angle.
76. ml1 ≠ 30; ml2 ≠ 15;
ml3 ≠ 75; ml4 ≠ 30
Lesson 6-3
2
80.
1
O
Can you conclude that the figure is a parallelogram?
Explain. 79–81. See margin.
79.
Lesson 3-7
a r
77. The radius is 19.3 mm. Find the apothem.
18.6 mm
78. Find the area of the 12-gon to the nearest
square millimeter. 1116 mm2
81.
Indicate whether each statement is always, sometimes, or never true.
82. Two nonvertical parallel lines have the same slope. always
83. Two perpendicular lines have slopes that are reciprocals. never
lesson quiz, PHSchool.com, Web Code: aua-1006
Lesson 10-6 Circles and Arcs
573
573