5-Minute Check on Lesson 10-15-Minute Check on Lesson 10-15-Minute Check on Lesson 10-15-Minute Check on Lesson 10-1 Transparency 10-2

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Refer to ⊙F.

1. Name a radius

2. Name a chord

3. Name a diameter

Refer to the figure and find each measure

4. BC

5. DE

6. Which segment in ⊙C is a diameter?Standardized Test Practice:

A CB DAC CD CB AB

FL, FM, FN, FO

LN, MO, MN, LO

LN, MO

3

13

D

D

AC

B

Lesson 10-2

Angles and Arcs

Objectives

• Recognize major arcs, minor arcs, semicircles, and central angles and their measures– central angles sum to 360°– major arcs measure > 180°– minor arcs measure < 180°– semi-circles measure = 180°

• Find arc length– Formula: C • (central angle / 360°)

% of circle that is the arc

Vocabulary

• Central Angle – has the center of the circle as its vertex and two radii as sides

• Arc – edge of the circle defined by a central angle

• Minor Arc – an arc with the central angle less than 180° in measurement

• Major Arc – an arc with the central angle greater than 180° in measurement

• Semicircle – an arc with the central angle equal to 180° in measurement

• Arc Length – part of the circumference of the circle corresponding to the arc

Circles - Arcsy

x

Central

Angle

Diameter (d)

Center

B

GF

E

H

BHG

BEG

Semi-CircleEHF

Circles - Probabilityy

xRadius (r)

Diameter (d)

Center

Circumference = 2πr = dπ

0°180°

90°

270°

135°

315°

Pie Charts Probability0 = no chance1 = for sure

135º ------ = 3/8360º or .375 or 37.5%

180º ------ = 1/2360º or .5 or 50%

45º ------ = 1/8360º or .125 or 12.5%

Find .

EXAMPLE 1

Substitution

Simplify.

Add 2 to each side.

Divide each side by 26.

Use the value of x to findGiven

Substitution

Answer: 52

The sum of the measures of

(CONT)

ALGEBRA Refer to .

Find .

EXAMPLE 2

Linear pairs are supplementary.

Substitution

Simplify.

Subtract 140 from each side.

form a linear pair.

Answer: 40

(CONT)

Answer: 65

Answer: 40

ALGEBRA AD and BE are diameters

a. Find m

b. Find m

EXAMPLE 3

Find .

In bisects and

is a minor arc, so

is a semicircle.

Answer: 90

EXAMPLE 4

Find .

In bisects and

since bisects .

is a semicircle.

Answer: 67

EXAMPLE 5

Find .

In bisects and

Answer: 316

EXAMPLE 6

Answer: 54

Answer: 72

In and are diameters, and bisects Find each measure.

a.

b.

c.

Answer: 234

EXAMPLE 7

In and .

a) Find the length of .

b) Find the length of arc DC.

In and . Write a proportion to compare each part to its whole.

degree measure of arcdegree measure of

whole circle

arc lengthcircumference

EXAMPLE 8

Example 2-4b

Now solve the proportion for .

Simplify.

Answer: The length of is units or about 3.14 units.

Multiply each side by 9 .

Answer: The length of arc DC is 7π/2 units or about 11 units.

C ∙ (% of the circle) = 9π ∙ (140/360)

= 7π/2

(CONT)

Summary & Homework

• Summary:– Sum of measures of central angles of a circle with

no interior points in common is 360°– Measure of each arc is related to the measure of

its central angle– Length of an arc is proportional to the length of

the circumference

• Homework: – pg 533-534; 14-23; 24-29; 32-35