Inscribed Angles and Arcs

Section 9.3Pg. 580

Mrs. Riggle

Objectives

Today we will learn how to:

• Define inscribed angle and intercepted arc.

• Use the Inscribed Angle Theorem and its corollaries.

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.

Measure of an Inscribed Angle

The measure of an inscribed angle is half the measure of its intercepted arc.

Central vs. Inscribed Angles

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.

Examples

Find the measure of the inscribed angle or intercepted arc.

Corollary

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

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.)

Closure

Refer to the circle in the figure with diameter MN. Find each measurement.

m <NABm arc MHBm arc HNm <MNHm arc MHN

Assignment

Independent Work

Pgs. 585–586 #11–31, odd

Work to be Submitted

9.3 EdMastery AssignmentDue 4p.m. Wednesday, April 13.

Ch. 8 exam due 4p.m. today!!!