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Geometry 10-6 Complete Lesson: Circles and Arcs

Last updated about 4 years ago

31 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

10

G.C.1

G.C.2

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G.CO.1

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10

10

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G.CO.1

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G.C.2

G.CO.1

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1.

Solve It! The bicycle wheel shown travels 63 in. in one complete rotation. It the wheel rotates only 120° about the center, how far does it travel? Enter your response in this format: "37 in."

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2.

Solve It! Explain your reasoning on the previous item.

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3.

Problem 1 Got It?

A

B

C

D

G.CO.1

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4.

Problem 1 Got It?

A

B

C

D

G.CO.1

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5.

Problem 1 Got It?

A

B

C

D

G.CO.1

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6.

Problem 2 Got It?

A

B

C

D

G.C.2

G.CO.1

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7.

Problem 2 Got It?

A

B

C

D

G.C.2

G.CO.1

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8.

Problem 2 Got It?

A

B

C

D

G.C.2

G.CO.1

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9.

Problem 2 Got It?

A

B

C

D

G.C.2

G.CO.1

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10.

Problem 3 Got It? A car has a circular turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. How much farther does a tire on the outside of the turn traven than a tire on the inside?

About 64.9 ft

About 101.1 ft

About 36.2 ft

About 29.5 ft

G.C.1

G.C.5

G.CO.1

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11.

Problem 3 Got It? Reasoning: Suppose the radius of ⊙A is equal to the diameter of ⊙B. What is the ratio of the circumference of ⊙A to the circumference of ⊙B?

2 : 1

π : 1

2π : 1

π : 2

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12.

Problem 4 Got It?

A

B

C

D

G.C.2

G.CO.1

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13.

A

B

C

D

G.CO.1

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14.

A

B

C

D

G.CO.1

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15.

A

B

C

D

G.CO.1

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16.

A

B

C

D

G.C.2

G.CO.1

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17.

A

B

C

D

G.C.2

G.CO.1

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18.

A

B

C

G.C.2

G.CO.1

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20.

Error Analysis: Your class must find the length of arc AB. A classmate submits the solution shown. What is her error?

G.C.2

G.CO.1

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21.

Review Lesson 10-5: Part of a regular dodecagon is shown. Match the numbered angles with their measures below.

∠1
∠2
∠3
∠4

15°
30°
75°

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22.

Review Lesson 10-5: The radius is 19.3 mm. What is the apothem? Respond in this format: "7.31 mm"

10

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25.

Review Lesson 6-3: Which figures can you conclude are parallelograms? Select all that apply.

null

null

null

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26.

Review Lesson 10-6: What is the circumference of a circle with diameter 17 in.?

8.5π

17π

8.5²π

17²π

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27.

Review Lesson 10-6: What is the length of a 90° arc in a circle with radius 6 cm?

≈ 3.14 cm

6 cm

≈ 6.28 cm

≈ 9.42 cm

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28.

Vocabulary Review: Respond to each question with Yes or No.

Yes
No

Is a circle a two-dimensional figure?
Is a circle a polygon?
Is every point on a circle the same distance from the center?

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29.

Use Your Vocabulary: Complete each sentence with the correct word from the list.

A minor arc is __?__ than a semicircle.
A major arc is __?__ than a semicircle.
You use __?__ points to name a major arc.
You use __?__ points to name a minor arc.

larger
smaller
two
three

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30.

Use Your Vocabulary: Classify the figures from the diagram.

arc KL
arc LJK

minor arc
major arc
semicircle
radius

G.CO.1

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31.

Reflection: Math Success

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23.

Review Lesson 10-5: What is the perimeter of the dodecagon to the nearest millimeter? Enter your response in this format: "21 mm"

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24.

Review Lesson 10-5: What is the area of the dodecagon to the nearest square millimeter? Enter your response in this format: "53 square millimeters"