11-2 Exercises
11-2
Exercises
KEYWORD: MG7 11-2
KEYWORD: MG7 Parent
GUIDED PRACTICE
Assignment Guide
Vocabulary Apply the vocabulary from this lesson to answer each question.
Assign Guided Practice exercises
as necessary.
1. An arc that joins the endpoints of a diameter is called a ? . (semicircle or
−−−−
major arc) semicircle
2. How do you recognize a central angle of a circle? Vertex is the center of the .
If you finished Examples 1–2
Basic 19–28, 33, 36
Average 19–28, 33, 34, 36
Advanced 19–28, 33, 34, 36, 54
If you finished Examples 1–4
Basic 19–40, 45, 47–50,
55–61
Average 19–51, 55–61
Advanced 19–44, 46–61
= 205°. Therefore ABC
is a
3. In P mABC
? . (major arc or minor arc) major arc
−−−−
4. In a circle, an arc that is less than a semicircle is a ? . (major arc or minor arc)
−−−−
minor arc
SEE EXAMPLE
Consumer Application Use the following information for Exercises 5–10.
1
p. 756
The circle graph shows how a typical
household spends money on energy.
Find each of the following.
5. m∠PAQ 162°
6. m∠VAU 25.2°
7. m∠SAQ 61.2°
36°
8. mUT
9. mRQ
Homework Quick Check
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Exercises: 20, 26, 30, 32, 38, 40
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SEE EXAMPLE
Find each measure.
2
129°
11. mDF
p. 757
270°
12. mDEB
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Find m∠EBF.
16. A B, and CD
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SEE EXAMPLE 4
p. 759
Multi-Step Find each length to the nearest tenth.
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18. EF
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KEYWORD: MG7 Resources
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3
p. 758
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14. mHLK
SEE EXAMPLE
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PRACTICE AND PROBLEM SOLVING
Independent Practice
For
See
Exercises Example
19–24
25–28
29–30
31–32
1
2
3
4
Extra Practice
Skills Practice p. S24
""
Sports Use the following information for Exercises 19–24.
The key shows the number of medals won
by U.S. athletes at the 2004 Olympics
in Athens. Find each of the following
i`>Ã
to the nearest tenth.
19. m∠ADB 122.3°
20. m∠ADC 101.4°
122.3°
21. mAB
136.3°
22. mBC
237.7°
23. mACB
223.7°
24. mCAB
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Application Practice p. S38
Find each measure.
152°
25. mMP
26. mQNL
155°
27. mWT
208°
28. mWTV
-
+ ÓnÂ
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1
6
Find m∠CAD.
EF.
CD
Data Collection For help
with Exercise 36, see
Technology Lab Activities.
Some suggestions for liquids are
muriatic acid, household lye and
ammonia, cola, white soda, diluted
and concentrated lemon juice, distilled water, salt water, orange juice,
household bleach, baking soda dissolved in water, antacid, vinegar, and
shampoo.
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29. A B, and
−− −−−
85°
30. JK LM. Find mJK.
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ÈnÂ
ÇÝÂ Inclusion Point out to students that, in Exercise 37,
∠DEA is a straight angle
and its measure is 180°.
Multi-Step Find each length to the nearest tenth.
31. CD
32. RS
6.6
+
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Ó°{
,
10.4
Some students may confuse the
number of medals won in
Exercises 19–24 with the angle
measures or percentages in the
circle graph. Remind students that
they have to first find the sum of
the gold, silver, and bronze medals.
Then they find each percentage and
calculate the central angle measures
before working the exercises.
7
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Determine whether each statement is true or false. If false, explain why.
33. A minor arc is 33. The central angle of a minor arc is an acute angle. F
always less than
34. Any two points on a circle determine a minor arc and a major arc. F
180°, so its central
∠ may be obtuse. 35. In a circle, the perpendicular bisector of a chord must pass through the center
of the circle. T
34. If the 2 pts.
36.
Data Collection Use a graphing calculator, a pH probe, and a data-collection
are the endpts.
device
to collect information about the pH levels of ten different liquids. Then
of a diam., they
create a circle graph with the following sectors: strong basic (9 < pH < 14), weak
determine 2
basic (7 < pH < 9), neutral (pH = 7), weak acidic (5 < pH < 7), and strong acidic
semicircles.
(0 < pH < 5).
36. Check students’ 37. In E, the measures of ∠AEB, ∠BEC, and ∠CED are in
graphs.
and mCD.
mBC,
the ratio 3 : 4 : 5. Find mAB,
45°; 60°; 75°
11-2 Arcs and Chords
761
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Lesson 11-2
761