Embed Size (px)
DESCRIPTION
Central Angles. Central Angle : An Angle whose vertex is at the center of the circle. ACB. AB. A. Major Arc. Minor Arc. More than 180°. Less than 180°. P. To name: use 3 letters. C. To name: use 2 letters. B. - PowerPoint PPT Presentation
Citation preview
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
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°
THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
Linear Pairs are Supplementary
Vertical Angles are Equal
Linear Pairs are Supplementary
http://www.mathopenref.com/linearpair.html
120° 60°
measure of an arc = measure of central angle
A
B
C
Q 96
m AB
m ACB
m AE
E
=
=
=
96°
264°
84°
Arc Addition PostulateA
B
C
m ABC =
m AB + m BC
Tell me the measure of the following arcs.
80100
40
140A
B
C
D
R
m DAB =
m BCA =
240
260
Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles.
4545
A
BC
D
110
Classwork
•Page 193 #9-18 You have 15 minutes.
Inscribed Angle: An angle whose
vertex is on the circle and
whose sides are chords of the circle
INSCRIBEDANGLE
INTER
CEP
TED
ARC
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
C
L
O
T1.
YES; CL
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
Q
R
K
V2. NO;
QVR
S
2
ArcdIntercepteAngleInscribed
160°
80°
To find the measure of an inscribed angle…
http://www.geogebra.org/
en/upload/files/english/Guy/
Circles_and_angles/Inscribed_Anlge.html
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!!
http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_angle_practice.html
Examples
3. If m JK = 80, find m <JMK.
M
Q
K
S
J
4. If m <MKS = 56, find m MS.
40
112
72
If two inscribed angles intercept the same arc, then they are congruent.
http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_angle_practice.html
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
Classwork:
•Page 193 #9-23•Page 207 #1-15
Whatever is left is homework
