Inscribed Angles Lesson 10.3bCalifornia 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

definitionsInscribed Polygon

A polygon with all of its vertices on a circle.Circumscribe

To circle around something.

A

B C

D

EF

P

hexagon is inscribed in

ABCDEFP

circumscribeshexagon

PABCDEF

example Find value of x and y.

8xo8xo

3yo

6yo

theoremInscribed Right Triangle

An inscribed right triangle has a diameter as its hypotenuse.

C

Q

P

R

is a right trianglePQR is a diameterPR

example

B

DA

C

Find the measure of the arc or angle.

180omADC

example

C

B

A

3xo

3 90x

30x

Find value of x.

theoremInscribed Quadrilateral

A quadrilateral can be inscribed in a circle if and only if its opposite angles are

supplementary.

S

Q

P

R

180

180

m P m R

m Q m S

85 180y 95y

100x 80 180x

example

TS

R85o

U80o

xo yo

Find value of x and y.

220 190 1800760 190 3420

x yx y

22 19 180x y

example

B

A

D

22xo

C40xo10yo

19yo

Find value of the measure of each angle.

3x 540 1620x

40 10 180x y -10( )19 ( )

22(3) 66m D

40(3) 120m C

example

B

A

D

22xo

C40xo10yo

19yo

Find value of the measure of each angle.

180 114m B m D

180 60m A m C

120o

66o

60o

114o

11

Today’s Assignment

Tribe Pride

always my best effort.

p.617: 16, 18 – 29

Find the value of each variable. Explain.

Can the quadrilateral always be inscribed in a circle? Explain your reasoning.