1. Circles
LESSON 7-6
Problem of the Day
In a bag of groceries, there are 6 tomatoes, 5 celery stalks, and 2 onions. What is the ratio of onions to tomatoes? What is the ratio of celery stalks
to onions?
2 : 6 or 1 : 3; 5 : 2
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2. Circles
LESSON 7-6
Additional Examples
Name all the radii, diameters, chords, and central angles shown in circle F.
central angles: BFA,
BFE,
and EFA
and CD
FE,
chords: EB
and FA
diameter: EB
radii: FB,
Quick Check
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3. Define:
Radius – a segment that connects a point on the circle with the center of the circle
Diameter – a segment that starts at a point on the circle, crosses the center, and reaches the other point of the circle
Central angle – an angle whose vertex is the center of the circle: two radii that make up an angle; is composed of two segments that meet at the center
Chord – segment with both ends on the circle

4. Name three of the arcs in circle F.
Circles
LESSON 7-6
Additional Examples
Name three of the arcs in circle F.
and BCE
AE,
AB,
Sample answer: Three arcs are
Quick Check
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5. Name two different arcs between points C and D.
Circles
LESSON 7-6
Additional Examples
Name two different arcs between points C and D.
The larger arc is CBD.
The shorter arc is CD.
Quick Check
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6. Define:
Arc – part of the circle
Semicircle – an arc that is half of the circle
Are all semicircles considered arcs? Yes
Are all arcs considered semicircles? No

7. Use circle O for questions 1–3.
Circles
LESSON 7-6
Lesson Quiz
Use circle O for questions 1–3.
1. Name the radii, diameter, and chords.
2. Name two central angles.
3. Name three arcs.
radii: OQ, OR, OS; diameter: QS;
chords: PQ, PR, QR, SQ
Sample: SOR, QOR
Sample: PQ, QRS, SP
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8. 1. Vocabulary Review How is finding the percent of a
Circle Graphs
LESSON 7-7
Check Skills You’ll Need
(For help, go to Lesson 6-4.)
1. Vocabulary Review How is finding the percent of a
number like multiplying decimals?
Find each answer.
2. 25% of % of % of 360
Check Skills You’ll Need
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9. 1. Every percentage can be written as a decimal by moving the decimal
Circle Graphs
LESSON 7-7
Check Skills You’ll Need
Solutions
1. Every percentage can be written as a decimal by moving the decimal
point two places to the left. Thus 25% becomes So taking the
percentage of a number is the same as multiplying by a decimal.
2. 25% = % = % = 0.72
• 360 = • 360 = • 360 = 259.2 1 4 1 4
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10. Use the circle graph below.
Circle Graphs
LESSON 7-7
Additional Examples
Use the circle graph below.
a. What percent of the days were snowy?
13%
b. How many days were cloudy?
27% of 30 days = 0.27 • 30 = 8.1
8 days were cloudy.
Quick Check
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11. Use the information in the table to make a circle graph.
Circle Graphs
LESSON 7-7
Additional Examples
Use the information in the table to make a circle graph.
Size of U.S. Households (2000)
No. of People in Household
Number
(in thousands) 1 2 3 4
5 or more
26,724
34,666
17,152
15,309
10,854
Step 1 Add to find the total number of households.
26, , , , , ,705 (in thousands)
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12. Circle Graphs
LESSON 7-7
Additional Examples
Quick Check
(continued)
Step 2 For each central angle, set up a proportion to find the angle measure. Use a calculator to solve.
15,309
104,705 d
360
10,854 f
26,724 a =
34,666 b
17,152 c
a °
b °
c °
d °
f °
Keep track of how you are rounding the angles. Why?
Step 3 Draw a circle. Draw the central angles using the degrees found in Step 2. Label each section. Add a title. Add a key if necessary.
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13. The circle graph shows how a class of 48 students spends free time
LESSON 7-7
Lesson Quiz
The circle graph shows how a class of 48 students spends free time
after lunch.
1. What percent study or do
extracurricular activities?
2. How many students spend
time on extracurricular activities?
3. Find the measure of the central angle that you would draw to represent
15% in a circle graph.
39% 12
54º
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14. This week’s homework:
Thursday:
Lesson 7-6:
pp , #s 8-14, 17, 25, 27, 31
Friday:
Lesson 7-7:
pp , #s 7-10, 12-16, 19 (OK to use calculator)