Transcript Central Angle

CCGPS Geometry
UNIT QUESTION: What special
properties are found with the parts of
a circle?
Standard: MMC9-12.G.C.1-5,G.GMD.1-3
Today’s Question:
How do we use angle measures to
find measures of arcs?
Standard: MMC9-12.G.C.2
AGENDA
1. Notes on Circles
2. Notes on Central Angles
3. Homework Worksheet
C
Parts of a Circle
Circle – set of all
points _________
equidistant
from a given point
called the _____
center
of the circle.
Symbol:
C
CHORD:
A segment
whose
endpoints
are on the
circle
Radius
RADIUS:
P
Distance from
the center to
point on
circle
Diameter
P
DIAMETER:
Distance
across the
circle
through its
center
Also known as the
longest chord.
D = ?
r = ?
r = ?
D = ?
Use P to determine whether each
statement is true or false.
Q
1. RT is a diameter.False
R
2. PS is a radius. True
P
3. QT is a chord. True
T
S
Secant Line:
intersects the
circle at
exactly TWO
points
Tangent Line:
a LINE that intersects
the circle exactly ONE
time
Forms a
90°angle
with a radius
Point of Tangency:
The point where the
tangent intersects
the circle
Name the term that best describes the notation.
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
Arc length is proportional to “r”
Classwork
• Practice Worksheet
Homework:
• Practice Worksheet