Arcs and Chords lesson 10.2aCalifornia State

Standards

4: Prove theorems involving congruence and similarity

7: Prove/use theorems involving circles.

21: Prove/solve relationships with circles.

Lesson Goals

Find the measure of arcs in a circle using the definition of arc measure and the arc addition postulate.

ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

definitionsCentral Angle

An angle whose vertex is the center of a circle.

Minor ArcA section of the circle cut by a central angle

that measures less than 180o

The measure of an minor arc equals the measure of its central angle.

definitions

C

A

B

mAB m ACB

definitionsMajor Arc

A section of the circle that measures more than 180o.The measure of a major arc equals the difference

between 360o and the measure of its associated minor arc.

SemicircleAn arc with endpoints coinciding with the endpoints

of a diameter

definitions

C

A

B

D

360mADB mAB

definitions

C

P

Q

180mPQ

180omEHI

328omHIE

example

C

H

I

E

Find the measure of each arc.

148o

32omEH

mSE 118o

mSET 218o

mST

example

C

D

T

S

Find the measure of each arc.

82o

142o

60o

100o

E

m ACB m ECD

AB DE

definitions

Congruent ArcsArcs with the same measure within the same circle or congruent circles.

C

A

BD

E

because

mCE 70o

AB CE

mAB

You try Find the measure of each arc.

70o

D

A

E

110o

C

B

mBD

mAE

Yes

Is ? AE BD

example

C

B

D

A

E

210o

Find the measure of each arc.

150o

150o

example Find the measure of each arc.

36o

36o

144o

13

Today’s Assignment

Tribe Pride

always my best effort.

p. 607: 12 – 38

Determine whether the arc is a minor arc,a major arc, or a semicircle of circle R.

and are diameters. COPYthe diagram. Find the indicated measure.KN JL

Find the measure of the red arc. Use circle P to find the value of x. Then find the measure of the red arc.

35. Name 2 pairs of congruent arcs in #32 – 34. Explain your reasoning.