Inscribed Angles and Arcs

1. Inscribed Angles and Arcs Section 9.3 Pg. 580 Mrs. Riggle

2. Objectives • Today we will learn how to: • Define inscribed angle and intercepted arc. • Use the Inscribed Angle Theorem and its corollaries.

3. Inscribed Angle • An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. • An arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the intercepted arc of the angle.

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

5. Central Angle: Vertex at the center of the circle. The measure of the central angle equals the measure of the intercepted arc. Inscribed Angle: Vertex is on the circle. The measure of the inscribed angle is equal to half the measure of the intercepted arc. Central vs. Inscribed Angles

6. Examples • Find the measure of the inscribed angle or intercepted arc.

7. Corollary • If inscribed angles of a circle intercept the same arc, then the angles are congruent.

8. Corollary • If an inscribed angle intercepts a semicircle, then the angle is a right angle. • (Notice that this makes sense since the measure of an inscribed angle is half the measure of the intercepted arc.)

9. Closure • Refer to the circle in the figure with diameter MN. Find each measurement. • m <NAB • m arc MHB • m arc HN • m <MNH • m arc MHN

10. Independent Work Pgs. 585–586 #11–31, odd Work to be Submitted 9.3 EdMastery Assignment Due 4p.m. Wednesday, April 13. Ch. 8 exam due 4p.m. today!!! Assignment