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 • 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