Download Central Angle - PHA Math Central

Geometry
January 4, 2011

Take out: Pencil,
Homework, binder and
begin the Do Now
silently!
Objectives: SWBAT:
 Describe what central
and inscribed angles are
 Apply the relationship
between the angle and its
intercepted arc to find
missing angle and arc
measurements
Agenda



Do Now (10 min)
Angles in circles ppt
(10 min)
Practice using
conjectures (30 min)
Angles in a Circle
2
Central Angle
Definition: An angle whose vertex lies on the center of the circle.
Central
Angle
(of a circle)
Central
Angle
(of a circle)
NOT A
Central
Angle
(of a circle)
3
Central Angle Theorem
The measure of a central angle is equal to the measure of the
intercepted arc.
Intercepted Arc
Central Angle
O
Y
110
Z
4
Central Angle Theorem
The measure of a central angle is equal to the measure of the
intercepted arc.
Example: Give AD is the diameter, find the
value of x and y and z in the figure.
B
25
A
C
x
y
O
55
z
D
x  25
y  180  (25  55 )  180  80  100
z  55
5
Inscribed Angle
Inscribed Angle: An angle whose vertex lies on a circle and whose
sides are chords of the circle (or one side tangent to the circle).
ABC is an inscribed angle.
No!
B
O
Examples:
1
C
A
D
3
2
Yes!
No!
4
Yes!
6
Intercepted Arc
Intercepted Arc: An angle intercepts an arc if and only if each of
the following conditions holds:
1. The endpoints of the arc lie on the angle.
2. All points of the arc, except the endpoints, are in the interior of the
angle.
3. Each side of the angle contains an endpoint of the arc.
C
B
ADC is the int ercepted arc of ABC.
O
A
D
7
Inscribed Angle Theorem
The measure of an inscribed angle is equal to ½ the measure of the
intercepted arc.
Y
Inscribed Angle
A
55
C
D
Z
Intercepted Arc
B
An angle formed by a chord and a tangent can be considered an
inscribed angle.
mAB
mABC 
2
8
An angle inscribed in a semicircle is a
right angle.
P
S
180
90
R
9