Geometry 10-6 Circles and Arcs

by Matthew Richardson

| 31 QuestionsNote from the author:

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.

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1

10 pts

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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10 pts

Solve It! Explain your reasoning on the previous item.

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10 pts

Problem 1 Got It?

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10 pts

Problem 1 Got It?

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10 pts

Problem 1 Got It?

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6

10 pts

Problem 2 Got It?

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10 pts

Problem 2 Got It?

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8

10 pts

Problem 2 Got It?

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10 pts

Problem 2 Got It?

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10 pts

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

11

10 pts

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

10 pts

Problem 4 Got It?

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10 pts

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10 pts

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10 pts

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10 pts

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10 pts

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10 pts

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10 pts

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

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10 pts

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°

22

10 pts

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

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10 pts

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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10 pts

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"

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10 pts

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

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10 pts

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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10 pts

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

28

10 pts

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?

29

10 pts

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

10 pts

Use Your Vocabulary: Classify the figures from the diagram.

- arc KL
- arc LJK

- minor arc
- major arc
- semicircle
- radius

31

10 pts

Reflection: Math Success

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