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Angles

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Objectives

• At the completion of the lesson, you will be able to…

• Define and identify arcs and central angles in circles

• Calculate the measures of arcs and central angles in circles

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Using Arcs of Circles

Central Angle – an angle whose vertex is at the center of a circle

Major Arc – formed by two points on a circle and its measure is greater than 180; named with 3 endpoints

Minor Arc – formed by two points on a circle whose measure is less than 180; named with 2 endpoints

central angle

minorarcmajor

arcP

B

A

C

Semicircle – an arc formed by two points on a circle whose measure is equal to 180

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Example: Naming Arcs

• Name:– minor arcs:

– major arcs:

– semicircles:

– An acute central angle:

– Two congruent arcs:

EH F

G

E

60°

60°

180°

•B

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Measuring arcs

Measure of an arc: equal to the measure of an arc’s central angleMinor arc:

Major arc – think about it: how would I find

EH F

G

E

60°

60°

180°

•B

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A postulate

Arc Addition Postulate

• The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs.

B

A

C

m = m + m ABC

AB

BC

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Ex. 1: Finding Measures of Arcs

• Find the measure of each arc of R.

a. b. c.

MNMPNPMN

PR

M

N80°

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Ex. 2: Finding Measures of Arcs

• Find the measure of each arc.

a. b. c.

GE

GEFR

EF

G

H

GF

40°

80°

110°

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Congruent arcs

• Arcs, in the same circle or in congruent circles, that have equal measures

C

D

A

BAB• and are in

the same circle and

m = m = 45°. So,

DC

ABDCDC

AB

45°

45°

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Homework

• Page 341 Classroom exercises 1-13

• Page 341 Written Exercises 1-8• Quiz tomorrow on 9.1-9.3