p a b c central angle : an angle whose vertex is at the center of the circle minor arcmajor arc less...
TRANSCRIPT
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P
A
BC
Central Angle : An Angle whose vertex is at the center of the
circleMinor ArcMajor Arc
Less than 180°
More than 180°
ABACB
To name: use 2 letters
To name: use 3 letters
<APB is a Central Angle
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P
E
F
D
Semicircle: An Arc that equals 180°
EDF
To name: use 3 letters
EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of
180°
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THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
Linear Pairs are Supplementary
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Vertical Angles are Equal
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Linear Pairs are Supplementary
http://www.mathopenref.com/linearpair.html
120° 60°
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measure of an arc = measure of central angle
A
B
C
Q 96
m AB
m ACB
m AE
E
=
=
=
96°
264°
84°
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Arc Addition PostulateA
B
C
m ABC =
m AB + m BC
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Tell me the measure of the following arcs.
80100
40
140A
B
C
D
R
m DAB =
m BCA =
240
260
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Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles.
4545
A
BC
D
110
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Classwork
•Page 193 #9-18 You have 15 minutes.
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Inscribed Angle: An angle whose
vertex is on the circle and
whose sides are chords of the circle
INSCRIBEDANGLE
INTER
CEP
TED
ARC
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Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
C
L
O
T1.
YES; CL
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Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
Q
R
K
V2. NO;
QVR
S
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2
ArcdIntercepteAngleInscribed
160°
80°
To find the measure of an inscribed angle…
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http://www.geogebra.org/
en/upload/files/english/Guy/
Circles_and_angles/Inscribed_Anlge.html
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120
x
What do we call this type of angle?What is the value of x?
y
What do we call this type of angle?How do we solve for y?The measure of the inscribed angle is HALF the
measure of the inscribed arc!!
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http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_angle_practice.html
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Examples
3. If m JK = 80, find m <JMK.
M
Q
K
S
J
4. If m <MKS = 56, find m MS.
40
112
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72
If two inscribed angles intercept the same arc, then they are congruent.
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http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_angle_practice.html
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Example 5
In J, m<A= 5x and m<B = 2x + 9.Find the value of x.
A
Q
D
JT
U
B
m<A = m<B 5x = 2x+9x = 3
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Classwork:
•Page 193 #9-23•Page 207 #1-15
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Whatever is left is homework