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Splash Screen. Five-Minute Check (over Lesson 10–1) Then/Now New Vocabulary Key Concept: Sum of Central Angles Example 1: Find Measures of Central Angles Key Concept: Arcs and Arc Measure Example 2: Classify Arcs and Find Arc Measures Theorem 10.1

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Presentation Transcript
lesson menu

Five-Minute Check (over Lesson 10–1)

Then/Now

New Vocabulary

Key Concept: Sum of Central Angles

Example 1: Find Measures of Central Angles

Key Concept: Arcs and Arc Measure

Example 2: Classify Arcs and Find Arc Measures

Theorem 10.1

Example 3: Real-World Example: Find Arc Measures in Circle Graphs

Postulate 10.1: Arc Addition Postulate

Example 4: Use Arc Addition to Find Measures of Arcs

Key Concept: Arc Length

Example 5: Find Arc Length

Lesson Menu
5 minute check 1
A

B

C

D

Name a radius.

A.

B.

C.

D.

5-Minute Check 1
5 minute check 2
A

B

C

D

Name a chord.

___

A.LF

B.MF

C.OM

D.NF

___

___

___

5-Minute Check 2
5 minute check 3
A

B

C

D

Name a diameter.

____

A.OM

B.OL

C.NF

D.MF

___

___

____

5-Minute Check 3
5 minute check 4
A

B

C

D

Refer to the figure. Find BC.

A. 2

B. 3

C. 4

D. 5

5-Minute Check 4
5 minute check 5
A

B

C

D

Refer to the figure. Find DE.

A. 9

B. 11

C. 13

D. 15

5-Minute Check 5
5 minute check 6
A

B

C

D

Find the length of the radius of the circle.

A. 6.5 in.

B. 10.9 in.

C. 13 in.

D. 17 in.

5-Minute Check 6
then now

You measured angles and identified congruent angles. (Lesson 1–4)

  • Identify central angles, major arcs, minor arcs, and semicircles, and find their measures.
  • Find arc lengths.
Then/Now
vocabulary

central angle

  • arc length
  • arc
  • minor arc
  • major arc
  • semicircle
  • congruent arcs
  • adjacent arcs
Vocabulary
example 11

The sum of the measures of

Find Measures of Central Angles

Substitution

Simplify.

Add 2 to each side.

Divide each side by 26.

Answer:x = 7

Example 1
example 12
A

B

C

D

Find the value of x.

A. 9

B. 10

C. 11

D. 65

Example 1
example 2

Answer:

Classify Arcs and Find Arc Measures

Example 2
example 22

Answer:

Classify Arcs and Find Arc Measures

Example 2
example 23

Answer:

Classify Arcs and Find Arc Measures

Example 2
example 24
A

B

C

D

A.

B.

C.

D.

Example 2
example 25
A

B

C

D

A.

B.

C.

D.

Example 2
example 26
A

B

C

D

A.

B.

C.

D.

Example 2
example 3

Answer:

Find Arc Measures in Circle Graphs

mLPK = 0.21(360) Find 21% of 360.

= 75.6 Simplify.

Example 3
example 32

Answer:

Find Arc Measures in Circle Graphs

Sum of arc in circle is 360.

Substitution

Simplify.

Simplify.

Example 3
example 33
A

B

C

D

A. 124.3

B. 140.4

C. 155.6

D. 165.9

Example 3
example 34
A

B

C

D

A. 273.6

B. 240.5

C. 215.7

D. 201.4

Example 3
example 4

.

Use Arc Addition to Find Measures of Arcs

Example 4
example 41

Answer:

Use Arc Addition to Find Measures of Arcs

Arc Addition Postulate

= mLH + mHI

Substitution

= 58 + 32

= 90

Example 4
example 43

Answer:

Use Arc Addition to Find Measures of Arcs

Arc Addition Postulate

= mIJ + mJK

Substitution

= 90 + 58

= 148

Example 4
example 44
A

B

C

D

A. 38

B. 52

C. 90

D. 180

Example 4
example 45
A

B

C

D

A. 52

B. 90

C. 142

D. 180

Example 4
example 5

cm

Use a calculator.

Answer:

Find Arc Length

Arc Length Equation

Substitution

Example 5
example 51

Answer:

Find Arc Length

Arc Length Equation

Substitution

Use a calculator.

Example 5
example 52

Answer:

Find Arc Length

Arc Length Equation

Substitution

Use a calculator.

Example 5
example 53
A

B

C

D

A. 3.56 cm

B. 3.77 cm

C. 3.98 cm

D. 4.21 cm

Example 5
example 54
A

B

C

D

A. 36.56 cm

B. 37.79 cm

C. 38.61 cm

D. 40.21 cm

Example 5
example 55
A

B

C

D

A. 32.99 cm

B. 33.59 cm

C. 33.89 cm

D. 34.61 cm

Example 5