Inscribed Angles Lesson 10.3aCalifornia State

Standards

4: Prove theorems involving congruence and similarity7: 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

definitionInscribed Angle

An angle whose vertex is on a circle and whose sides contain chords of the circle.

P

QR

definitionIntercepted Arc

An arc that lies in the interior of an inscribed angle

and has endpoints on the angle.P

QR

12 mAB

theoremInscribed Angle Measure

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

C

A

B

m ACB

D

example

B

C

140o70o

Find the measure of the arc or angle.

A

mAC

C

theoremCongruent Inscribed Angles

Inscribed anglesare congruent.

B

A

E AAEB CB

that intercept the same arc

m ADE

m ACE

m ABE

example

CB

D

A

E90o

45o

45o

45o

Find the measure of the arc or angle.

example

B

A

C98o

196o

Find the measure of the arc or angle.

m ABC

D

m C

example

CB

D

44o44o

Find the measure of the arc or angle.

A

m PON

60o

35o

130o

90o

11

Today’s Assignment

Tribe Pride

always my best effort.

p. 616: 6, 7, 9 – 15, 17, 35, 43

Find the measure of the blue arc or angle.

Find the value of each variable. Explain.