8-2a arcs and central angles
DESCRIPTION
8-2A Arcs and Central Angles. What is a central angle? How are arcs defined? What is a major arc? What is a minor arc? What is the measure of a semicircle?. Circles Graphs. Turn to page 564 in your book and look at the land areas of continents. Central angles. - PowerPoint PPT PresentationTRANSCRIPT
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8-2A Arcs and Central Angles
What is a central angle?
How are arcs defined?
What is a major arc?
What is a minor arc?
What is the measure of a semicircle?
![Page 2: 8-2A Arcs and Central Angles](https://reader036.vdocuments.us/reader036/viewer/2022062804/56814930550346895db67161/html5/thumbnails/2.jpg)
Circles Graphs
Turn to page 564 in your book and look at the land areas of continents.
![Page 3: 8-2A Arcs and Central Angles](https://reader036.vdocuments.us/reader036/viewer/2022062804/56814930550346895db67161/html5/thumbnails/3.jpg)
Central angles
Central angles are angles whose vertices are at the center of the circle.
Central angle
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Arcs—parts of a circle
There are three kinds of arcs made by central angles:
Major arcs: greater than 180°
Named with 3 letters
Minor arcs: less than 180°
Named with 2 letters
Semi-circles: exactly 180°
Named with 3 letters
one-half of a circle
A
B
C
D
Major arc ADB
A BC
D
Minor arc AB
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Measures in Degrees
• Complete circle measures 360°.
• The measure of any semicircle is 180°.
(½ of a circle)
360°
A
B
C180°
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Measures
• Measure of a minor arc is equal to the measure of the central angle.
• Measure of the major arc is equal to 360° minus the measure of its minor arc.
W
X
Y
Z
80°
XY
Z
W
80°mXZY = 360°−mWX
XWmWXYm
80
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Find each arc measure in ּסL
• mMN
• mMPN
• mPQN
P
M
N
Q
L 54°
54°
306°
180°
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Arc-Additional TheoremThe measure of two
adjacent, nonoverlapping arcs is the sum of the measures of the two arcs.
That is if C is on arc AB, then mAB = mAC + mCB
A
B
C
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Find each arc measure.• mRST
• mDE
• mHGF
R
S
T
D
E
H
G
F
40°
60°
153°
38°
320°
120°
191°
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Definition
Congruent arcs are arcs in the same circle (or congruent circles) that have the same measure.
A
BX
Y
60° 60°
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• What is a central angle?
Central angles are angles whose vertices are at the center of the circle.
How are arcs defined?
Arcs are defined as major arcs, minor arcs and semi circles.
• What is a major arc?
An arc that is greater than 180°• What is a minor arc?
An arc that is less than 180°• What is the measure of a semicircle?
Exactly 180°.
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