Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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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
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MG3.1 Identify and construct basic elements of
geometric figures (e.g., altitudes, midpoints,
diagonals, angle bisectors, and perpendicular
bisectors central angles, radii, diameters, and
chords of circles) by using a compass and
straightedge.
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Vocabulary
circle center of a circle arc radius diameter chor
d central angle sector
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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. This distance is called
the radius of the 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.
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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
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Additional Example 1 Identifying Parts of Circles
Name the parts of circle M.
N
A. radii
O
P
B. diameters
M
Q
C. chords
R
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Check It Out! Example 1
Name the parts of circle M.
B
A
C
A. radii
G
B. diameters
D
H
F
C. chords
E
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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.
Sector
)
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
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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.
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Additional Example 2 Continued
List the important information The percent of
people whose favorite muffin is blueberry is
40.
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Additional Example 2 Continued
The central angle measure of the sector that
represents this group is 40 of the angle measure
of the whole circle. The angle measure of a
circle is 360. 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
0.40 360 144
Multiply.
The central angle of the sector measures 144.
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Additional Example 2 Continued
Look Back
The 40 sector is less than half the graph, and
144 is less than half of 360. Since 144 is
close to 180, the answer is reasonable.
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Check It Out! Example 2
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 banana nut.
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Check It Out! Example 2 Continued
List the important information The percent of
people whose favorite muffin is banana nut is
35.
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Check It Out! Example 2 Continued
The central angle measure of the sector that
represents this group is 35 of the angle measure
of the whole circle. The angle measure of a
circle is 360. Since the sector is 35 of the
circle graph, the central angle measure is 35 of
the 360 in the circle.
35 of 360 0.35 360
0.35 360 126
Multiply.
The central angle of the sector measures 126.
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Check It Out! Example 2 Continued
Look Back
The 35 sector is about one-third the graph, and
126 is about one-third of 360. Since 126 is
close to 120, the answer is reasonable.
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Lesson Quiz
Name the parts of circle B. 1. radii 2.
diameter(s) 3. chord(s) 4.
A pie is cut into 8 equal sectors. Find the
measure of the central angle of one slice of pie.
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