Five-Minute Check (over Lesson 10–1)

NGSSS

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

Over Lesson 10–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Name a radius.

A.

B.

C.

D.

Over Lesson 10–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Name a chord.

A. LF

B. MF

C. OM

D. NF

___

___

___

___

Over Lesson 10–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Name a diameter.

A. OM

B. OL

C. NF

D. MF

___

____

____

___

Over Lesson 10–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 2

B. 3

C. 4

D. 5

Refer to the figure. Find BC.

Over Lesson 10–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 9

B. 11

C. 13

D. 15

Refer to the figure. Find DE.

Over Lesson 10–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 6.5 in.

B. 10.9 in.

C. 13 in.

D. 17 in.

Find the length of the radius of the circle.

MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

MA.912.G.6.4 Determine and use measures of arcs and related angles.

Also addresses MA.912.G.6.3 and MA.912.G.6.5.

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.

• central angle

• arc

• minor arc

• major arc

• semicircle

• congruent arcs

• adjacent arcs

• arc length

Find Measures of Central Angles

Find the value of x.

Find Measures of Central Angles

Substitution

Simplify.

Add 2 to each side.

Divide each side by 26.

The sum of the measures of

Answer: x = 7

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 9

B. 10

C. 11

D. 65

Find the value of x.

Classify Arcs and Find Arc Measures

Answer:

Classify Arcs and Find Arc Measures

Classify Arcs and Find Arc Measures

Answer:

Classify Arcs and Find Arc Measures

Answer:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A.

B.

C.

D.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A.

B.

C.

D.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A.

B.

C.

D.

Find Arc Measures in Circle Graphs

mLPK = 0.21(360) Find 21% of 360.

= 75.6 Simplify.

Answer:

Find Arc Measures in Circle Graphs

Find Arc Measures in Circle Graphs

Sum of arc in circle is 360.

Substitution

Simplify.

Simplify.

Answer:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 124.3

B. 140.4

C. 155.6

D. 165.9

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 273.6

B. 240.5

C. 215.7

D. 201.4

Use Arc Addition to Find Measures of Arcs

.

Use Arc Addition to Find Measures of Arcs

Arc Addition Postulate

Substitution= 58 + 32

= mLH + mHI

= 90

Answer:

Use Arc Addition to Find Measures of Arcs

Use Arc Addition to Find Measures of Arcs

Arc Addition Postulate

Substitution= 90 + 58

= mIJ + mJK

= 148

Answer:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 38

B. 52

C. 90

D. 180

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 52

B. 90

C. 142

D. 180

Find Arc Length

Arc Length Equation

Substitution

Answer:

Use a calculator.cm

Find Arc Length

Arc Length Equation

Substitution

Use a calculator.

Answer:

Find Arc Length

Arc Length Equation

Substitution

Use a calculator.

Answer:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3.56 cm

B. 3.77 cm

C. 3.98 cm

D. 4.21 cm

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 36.56 cm

B. 37.79 cm

C. 38.61 cm

D. 40.21 cm

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 32.99 cm

B. 33.59 cm

C. 33.89 cm

D. 34.61 cm