8-3A Inscribed Angles

1
8-3A Inscribed Angles

• What is an inscribed angle?
• What is the relationship between an inscribed
  angle and its intercepted arc?

2
Find the measure of each arc
54 180 306
E

• mDE
• mAED
• mEBD

54
A
D
C
B
What kind of angle is angle ECD? Central angle
3
Definition

• His name was inscribed on the award.
• The square is inscribed in the circle.

An inscribed angle is an angle with its vertex on
a circle and sides that contain chords of the
circle.
4
Sizing Up Inscribed Angles
A

• Measure the central angle
• What is the measure of the arc AB?
• Measure the inscribed angle
• Compare the measure of the central angle and the
  inscribed angle.

C
B
D
5
Inscribed Angle Theorem

• The measure of an inscribed angle is half the
  measure of its intercepted arc.

A
C
B
6
Find the measure of each angle or arc indicated
by a variable.
x
C
24
z
160
48
90
y
80
7
Theorem

• If two inscribed angles intercept the same arc,
  then they are congruent.

A
D
B
C
8
Theorem

• An inscribed angle that intercepts a semicircle
  is a right angle.

9

• What is an inscribed angle?
• An inscribed angle is an angle with its vertex on
  a circle and sides that contain chords of the
  circle.
• What is the relationship between an inscribed
  angle and its intercepted arc?
• The measure of an inscribed angle is half the
  measure of its intercepted arc.

10
Assignment 8-3A

• Page 586, 1-6, 8-12, 29-36