1. Inscribed Angles Lesson 10.3b 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

2. definitions Inscribed Polygon A polygon with all of its vertices on a circle. Circumscribe To circle around something. A B C D E F P

3. example Find value of x and y. 8xo8xo 8xo8xo 3yo3yo 6yo6yo

4. theorem Inscribed Right Triangle An inscribed right triangle has a diameter as its hypotenuse. C Q P R

5. example B D A C Find the measure of the arc or angle. 180 o

6. example C B A 3xo3xo Find value of x.

7. theorem Inscribed Quadrilateral A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. S Q P R

8. example T S R 85 o U 80 o xoxo yoyo Find value of x and y.

9. example B A D 22 x o C 40 x o 10 y o 19 y o Find value of the measure of each angle. -10( ) 19 ( )

10. example B A D 22 x o C 40 x o 10 y o 19 y o Find value of the measure of each angle. 120 o 66 o 60 o 114 o

11. 11 Today’s Assignment  p.617: 16, 18 – 29

12. Find the value of each variable. Explain. Can the quadrilateral always be inscribed in a circle? Explain your reasoning.