8-3A Inscribed Angles

What is an inscribed angle?

What is the relationship between an inscribed angle and its

intercepted arc?

Find the measure of each arc

• mDE

• mAED

• mEBDA

B

C

D

E

54°

54°

180°

306°

What kind of angle is angle ECD?

Central angle

DefinitionHis name was inscribed on the award.

The square is inscribed in the circle.

A

B

CAn inscribed angle is an angle with its vertex on a circle and sides that contain chords of the circle.

Sizing Up Inscribed Angles

• Measure the central angle

• What is the measure of the arc AB?

• Measure the inscribed angle

• Compare the measure of the central angle and the inscribed angle.

A

BC

D

ACB

ADB

Inscribed Angle Theorem

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

A

B

C

Find the measure of each angle or arc indicated by a variable.

24°

x°

160°

y°

C

z°

48°

80°

90°

Theorem

If two inscribed angles intercept the same arc, then they are congruent.

A

B

C

D

Theorem

An inscribed angle that intercepts a semicircle is a right angle.

• What is an inscribed angle?

An inscribed angle is an angle with its vertex on a circle and sides that contain chords of the circle.

• What is the relationship between an inscribed angle and its intercepted arc?

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

Assignment 8-3A

Page 586, 1-6, 8-12, 29-36