Warm-Up
1.
The measurements of two vertical angles are 15x
and 10x+15. What is the measurement of each
angle?
Day 24
Circles: Vocab & Central
Angles
TODAY’S QUESTION: HOW DO WE USE
ANGLE MEASURES TO FIND MEASURES OF
ARCS? (MMC9-12.G.C.2)
AGENDA
1.
2.
3.
4.
Notes on Circles
Notes on Central Angles
Practice Worksheet
Homework Worksheet
C
Circle
The set of all points that are
equidistant
__________ from a reference
center
point, the ________.
The set of points from a 2dimensional curve that
measures360
___.
Symbol:
C
CHORD:
segement
A __________whose
endpoints lie on
__________
the circumference
of the circle.
Diameter A straight line passing
P
center of
through the _______
a circle connecting two
points on the circle;
twice the
equal to ______
radius.
Also known as the
longest chord.
Radius
P
The distance from
center to a
the ______
point on the
______
circle; equal to
half
____ the diameter.
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:
A line that
intersects a circle
TWO
at exactly _____
points.
Tangent Line:
a LINE that intersects a
ONE point
circle at exactly ____
PERPENDICULAR
and is ____________
to
the radius of the circle.
Forms a 90°angle
with a radius
Point of Tangency:
The point where the
tangent intersects
the circle
Point of Tangency
Where the tangent
TOUCHES
line ___________ the
circle.
Name the term that best describes the notation.
arc that is half
Semicircle: An ____
____ of a circle.
E
D
To name: use
3 letters
EDF
P
F
Measures
EQUATLY 180°.
Major Arc
Minor Arc
More than 180°
P
ACB
To name: use
3 letters
Less than 180°
A
AB
C
Part of a circle’s
circumference that
GREATER than
is ________
its semicircle.
B
To name: use
2 letters
Part of a circle’s
circumference that
LESS than its
is ____
semicircle.
Central Angle :
vertex at the center
An Angle with its ______
_____ of the circle
A
P
C
B
APB is a Central Angle
measure of an arc = measure of central angle
A
E
Q
m AB = 96°
m ACB = 264°
m AE = 84°
96
B
C
Example 1
Always Remember
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
Linear Pairs total 180°.
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
Example 2
140
R
40
100
80
B
A
angle
Two arcs that have the same ______
measurement and are either of the same
circle or two congruent circles.
C
B
45
A
45
D
110
Arc length is proportional to “r”