1. 11-3 Inscribed 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 TheoremP ao
60o T Q
30o S bo
60o R

5. Corollaries to the Inscribed Angle Theorem
Two inscribed angles that intercept the same arc are congruent.
An angle inscribed in a semicircle is a right angle.
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
55o xo L K