Download 10.2-central-angles

Analytic Geometry 10/21
UNIT QUESTION: What special
properties are found with the parts of
a circle?
Today’s Question:
How do we use angle measures to
find measures of arcs?
Central Angle :
An Angle whose vertex is at the center of the circle
A
Major Arc
Minor Arc
More than 180°
Less than 180°
P
ACB
To name: use
3 letters
AB
C
B
<APB
is a Central Angle
To name: use
2 letters
Semicircle: An Arc that equals 180°
E
D
To name: use
3 letters
EDF
P
F
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
E
Q
m AB = 96°
m ACB = 264°
m AE = 84°
96
B
C
Arc Addition Postulate
A
C
B
m ABC = m AB + m BC
Tell me the measure of the following arcs.
m DAB = 240
m BCA = 260
D
C
140
R
40
100
80
B
A
Congruent Arcs have the same measure and
MUST come from the same circle or of
congruent circles.
C
B
45
A
45
D
110