Inscribed Angles Lesson 10.3a

1. Inscribed Angles Lesson 10.3a California State Standards Lesson Goals Find the measures of arcs and angles within a circle by using the Inscribed Angle Measure Theorem and the Congruent Inscribed Angles Theorem. • 4: Prove theorems involving congruence and similarity • 7: Prove/use theorems involving circles. • 21: Prove/solve relationships with circles. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

2. definition Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle. P inscribed angle Q R

3. definition Intercepted Arc An arc that lies in the interior of an inscribed angle and has endpoints on the angle. P intercepted arc Q R

4. theorem • Inscribed Angle Measure • The measure of an inscribed angle • is half the measure of its intercepted arc. A B C

5. example Find the measure of the arc or angle. B 140o 70o A C D

6. theorem Congruent Inscribed Angles Inscribed angles are congruent. that intercept the same arc B E A C

7. example Find the measure of the arc or angle. C B 45o 45o A 45o D 90o E

8. example Find the measure of the arc or angle. B 98o C A 196o D

9. example Find the measure of the arc or angle. C B 44o 44o A D

10. 60o 35o 130o 90o

11. Today’s Assignment • p. 616: 6, 7, 9 – 15, 17, 35, 43 Tribe Pride always my best effort.

12. Find the measure of the blue arc or angle. Find the value of each variable. Explain.