Inscribed Angles Lesson 10.3a California State Standards 4: Prove theorems involving congruence and similarity 7: Prove/use theorems involving circles. 21: Prove/solve relationships with circles. 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. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

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

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

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

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

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

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

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

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

60 o 35 o 130 o 90 o

11 Today’s Assignment  p. 616: 6, 7, 9 – 15, 17, 35, 43

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