1. 8-4 Properties of Circles Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 8-4 Properties of Circles Warm Up
Course 2
8-4
Properties of Circles
Warm Up
1. Two angles are supplementary. One angle measures 61°. Find the measure of the other angle.
2. Two angles are complementary. One angle measures 19°. Find the measure of the other angle.
3. Two angles are supplementary and congruent. Find the measure of each angle.
119°
71°
90°

3. 8-4 Properties of Circles Problem of the Day
Course 2
8-4
Properties of Circles
Problem of the Day
In a circle graph, three sectors representing 15%, 25%, and 30% are labeled. What percent does the fourth sector represent, and what is its measure in degrees?
30%; 108°

4. 8-4 Properties of Circles
Course 2
8-4
Properties of Circles
Learn to identify parts of a circle and to find central angle measures.

5. Insert Lesson Title Here
Course 2
8-4
Properties of Circles
Insert Lesson Title Here
Vocabulary
circle
center of a circle
radius
diameter
chord
arc
central angle
sector

6. 8-4 Properties of Circles
Course 2
8-4
Properties of Circles
A circle is the set of all points in a plane that are the same distance from a given point, called the center of a circle.
A circle is named by its center. For example, if point A is the center of a circle, then the name of the circle is circle A. There are special names for the different parts of a circle.

7. 8-4 Properties of Circles Diameter Arc
Course 2
8-4
Properties of Circles
Diameter
Arc
Part of a circle named by its endpoints
Line segment that passes
through the center of a circle, and whose endpoints lie on the circle
Radius
Line segment whose endpoints are the center
of a circle and any point on the circle
Chord
Line segment whose
endpoints are any two
points on a circle

8. Additional Example 1: Identifying Parts of a Circle
Course 2
8-4
Properties of Circles
Additional Example 1: Identifying Parts of a Circle
Name the parts of circle M. N
A. radii:
MN, MR, MQ, MO O P
B. diameters:
NR, QO M Q
C. chords:
NR, QO, QN, NP R
Radii is the plural form of radius.
Reading Math

9. 8-4 Properties of Circles Check It Out: Example 1
Course 2
8-4
Properties of Circles
Check It Out: Example 1
Name the parts of circle M. B A C
A. radii:
GB, GA, GF, GD G
B. diameters:
BF, AD D H F
C. chords:
AH, AB, CE,
BF, AD E

10. 8-4 Properties of Circles A central angle of a circle
Course 2
8-4
Properties of Circles
Sector
A central angle of a circle
is an angle formed by two
radii. A sector of a circle
is the part of the circle
enclosed by two radii and an
arc connecting them. )
The sum of the measures of all
of the central angles in a circle
is 360°. We say that there are
360° in a circle.
Central angle

11. 8-4 Properties of Circles
Course 2
8-4
Properties of Circles
Additional Example 2: Problem Solving Application
The circle graph shows the results of a survey about favorite types of muffins. Find the central angle measure of the sector that shows the percent of people whose favorite type of muffin is blueberry.

12. Understand the Problem
Course 2
8-4
Properties of Circles
Additional Example 2 Continued 1
Understand the Problem
The answer is the measure of the
central angle that represents blueberry.
List the important information:
• The percent of people whose favorite
muffin is blueberry is 40%.
• The central angle measure of the sector that represents this group is 40% of the 360° of the circle.

13. Additional Example 2 Continued
Course 2
8-4
Properties of Circles
Additional Example 2 Continued 2
Make a Plan
There are 360° in a circle. Since the sector is 40% of the circle graph, the central angle is 40% of the 360° in the circle.
40% of 360° = 0.40 · 360°
Solve 3
0.40 · 360° = 144°
Multiply.
The central angle of the sector is 144°.

14. Additional Example 2 Continued
Course 2
8-4
Properties of Circles
Additional Example 2 Continued 4
Look Back
The 40% sector is less than half the graph, and 144° is less than half of 360°. Therefore, the answer is reasonable.

15. 8-4 Properties of Circles Check It Out: Example 2
Course 2
8-4
Properties of Circles
Check It Out: Example 2
The circle graph shows the results of a survey about the favorite types of muffins. Find the central angle measure of the sector that shows the percent of people whose favorite type of muffin is banana nut.

16. Understand the Problem
Course 2
8-4
Properties of Circles
Check It Out: Example 2 Continued 1
Understand the Problem
The answer is the measure of the
central angle that represents banana nut.
List the important information:
• The percent of people whose favorite
muffin is banana nut is 35%.
• The central angle measure of the sector that represents this group is 35% of the 360° of the circle.

17. Check It Out: Example 2 Continued
Course 2
8-4
Properties of Circles
Check It Out: Example 2 Continued 2
Make a Plan
There are 360° in a circle. Since the sector is 35% of the circle graph, the central angle is 35% of the 360° in the circle.
35% of 360° = 0.35 · 360°
Solve 3
0.35 · 360° = 126°
Multiply.
The central angle of the sector is 126°.

18. Check It Out: Example 2 Continued
Course 2
8-4
Properties of Circles
Check It Out: Example 2 Continued 4
Look Back
The 35% sector is less than half the graph, and 126° is less than half of 360°. Therefore, the answer is reasonable.

19. Insert Lesson Title Here
Course 2
8-4
Properties of Circles
Insert Lesson Title Here
Lesson Quiz
Name the parts of circle B.
1. radii
2. diameter(s)
3. chord(s) 4.
BA, BC AC
DE, FE, AC
A pie is cut into 8 equal sectors. Find the
measure of the central angle of one slice of
pie.
45°