SWBAT find the measure of an inscribed angle
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
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
let’s practice
•Page 606 #9-18 You have 7 minutes.You have 7 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
Let’s investigate
Page 607
2
ArcdIntercepteAngleInscribed
160°
80°
To find the measure of an inscribed angle…
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!!
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.
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
Let’s practice
•Page 611 #5-16
Homework
• Page 612 # 23 - 27