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Transparency 10-2. D. B. A. C. 5-Minute Check on Lesson 10-1. Refer to ⊙ F. Name a radius Name a chord Name a diameter Refer to the figure and find each measure 4. BC 5. DE 6. Which segment in ⊙ C is a diameter?. FL, FM, FN, FO.

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5-Minute Check on Lesson 10-1

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5 minute check on lesson 10 1

Transparency 10-2

D

B

A

C

5-Minute Check on Lesson 10-1

  • Refer to ⊙F.

  • Name a radius

  • Name a chord

  • Name a diameter

  • Refer to the figure and find each measure

  • 4. BC

  • 5. DE

  • 6. Which segment in ⊙C is a diameter?

FL, FM, FN, FO

LN, MO, MN, LO

LN, MO

3

13

Standardized Test Practice:

A

B

C

D

D

AB

AC

CD

CB

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


Lesson 10 2

Lesson 10-2

Angles and Arcs


Objectives

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

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 arcs

y

x

Circles - Arcs

Semi-CircleEHF

Major Arc

BEG

E

Diameter (d)

Center

CentralAngle

B

F

BHG

G

Minor Arc

H


Circles probability

y

x

Circles - Probability

Pie Charts

Probability0 = no chance1 = for sure

90°

135°

135º------ = 3/8

360º

or .375 or 37.5%

Diameter (d)

Radius (r)

180°

Center

45º------ = 1/8

360º

or .125 or 12.5%

180º------ = 1/2

360º

or .5 or 50%

315°

270°

Circumference = 2πr = dπ


Example 2 1a

Find .

Example 2-1a

ALGEBRA: Given Diameter RT


Example 2 1b

The sum of the measures of

Use the value of x to find

Example 2-1b

Substitution

Simplify.

Add 2 to each side.

Divide each side by 26.

Given

Substitution

Answer: 52


Example 2 1c

ALGEBRA Refer to .

Find .

Example 2-1c


5 minute check on lesson 10 1

form a linear pair.

Linear pairs are supplementary.

Substitution

Simplify.

Subtract 140 from each side.

Answer: 40


Example 2 1e

ALGEBRA AD and BE are diameters

a. Find m

b. Find m

Example 2-1e

Answer: 65

Answer: 40


Example 2 2a

In bisects and

is a minor arc, so

is a semicircle.

Find .

Example 2-2a

Answer: 90


Example 2 2c

In bisects and

since bisects .

Find .

is a semicircle.

Example 2-2c

Answer: 67


Example 2 2e

In bisects and

Find .

Example 2-2e

Answer: 316


Example 2 2g

In and are diameters, and bisects Find each measure.

a.

b.

c.

Example 2-2g

Answer: 54

Answer: 72

Answer: 234


Example 2 4a

degree measure of arc

In and . a) Find the length of .

b) Find the length of arc DC.

arc length

circumference

degree measure of whole circle

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

Example 2-4a


Example 2 4b

Now solve the proportion for .

Multiply each side by 9 .

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

Example 2-4b

Simplify.

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

= 7π/2

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


Summary homework

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; 14-19; 24-29; 32-35


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