1. Chapter 10 Circles Section 10.3 Inscribed Angles U SING I NSCRIBED A NGLES U SING P ROPERTIES OF I NSCRIBED P OLYGONS

2. U SING I NSCRIBED A NGLES An _____________ is an angle whose _____ is on a circle and whose ________________ of the circle. The arc that lies in the interior of an inscribed angle and has __________________ is called the _____________ of the angle.

3. THEOREM U SING I NSCRIBED A NGLES THEOREM 10.8 Measure of an Inscribed Angle If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc. C A B D

4. Find the measure of the blue arc or angle. Finding Measures of Arcs and Inscribed Angles N P M 100° C W X Y Z 115° C R S T Q C

5. THEOREM A D C B U SING I NSCRIBED A NGLES THEOREM 10.9 If two inscribed angles of a circle intercept the, then the angles are congruent.

6. U SING P ROPERTIES OF I NSCRIBED P OLYGONS If all of the vertices of a polygon lie on a circle, the polygon is __________ in the circle and the circle is _____________ about the polygon. The polygon is an inscribed polygon and the circle is a circumscribed circle.

7. U SING P ROPERTIES OF I NSCRIBED P OLYGONS THEOREMS ABOUT INSCRIBED POLYGONS THEOREM 10.10 If a ____________ is inscribed in a circle, then the ______________________ _______. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. C A B

8. U SING P ROPERTIES OF I NSCRIBED P LOYGONS THEOREMS ABOUT INSCRIBED POLYGONS THEOREM 10.11 A quadrilateral can be inscribed in a circle if and only if its ________ ______________________. C E D F G

9. Using an Inscribed Quadrilateral In the diagram, ABCD is inscribed in P. Find the measure of each angle.. P B C D A 2y ° 3y ° 5x ° 3x °

10. P B C D A 2y ° 3y ° 5x ° 3x ° Using an Inscribed Quadrilateral S OLUTION ABCD is inscribed in a circle, so opposite angles are supplementary.

11. Using an Inscribed Quadrilateral P B C D A 2y ° 3y ° 5x ° 3x °

12. Using an Inscribed Quadrilateral P B C D A 2y ° 3y ° 5x ° 3x °