11-3 Inscribed Angles

1
11-3Inscribed Angles

• Theorems
• Inscribed Angle Theorem, 11-10
• Corollaries
• Corollaries to the Inscribed Angle Theorem
• Vocabulary
• Inscribed angle, Intercepted arc

2
Vocabulary
A
Intercepted Arc
Inscribed Angle
C
B
3
Theorem 11-9 (Inscribed Angle Theorem)

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

A
B
C
4
1 Using the Inscribed Angle Theorem

P
ao
60o
T
Q
30o
S
bo
60o
R
5
Corollaries to the Inscribed Angle Theorem

1. Two inscribed angles that intercept the same arc
   are congruent.
2. An angle inscribed in a semicircle is a right
   angle.
3. The opposite angles of a quadrilateral inscribed
   in a circle are supplementary.

6
2 Using Corollaries to Find Angle Theorem

• Find the diagram at the right, find the measure
  of each numbered angle.

120o
1
60o
2
4
80o
3
100o
7
Theorem 11-10

• The measure of an angle formed by a tangent and a
  chord is half the measure of the intercepted arc.

B
B
D
D
C
C
8
3 Using Theorem 11-10

• Find x and y.

J
90o
Q
35o
yo
xo
55o
L
K