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9-12 Integrated Math 2 Unit 7 Lesson 14

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 •Integrated Math 2 Integrated Math 3

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 •Unit 7 Unit 8

Modeling Prompts

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 •Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

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9-12

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Integrated Math 2
Integrated Math 3

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Geometry
Algebra 2
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Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

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Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
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Unit 7, Lesson 14

Angles, Arcs, and Radii

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Integrated Math 2

Practice

Problem 1
Student Task Statement
Here are two circles. The smaller circle has radius , circumference , and diameter . The larger circle has radius , circumference , and diameter . The larger circle is a dilation of the smaller circle by a factor of .

Using the circles, write 3 pairs of equivalent ratios. Find the value of each set of ratios you wrote.

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Problem 2

Student Task Statement

Tyler is confident that all circles are similar, but he cannot explain why this is true. Help Tyler explain why all circles are similar.

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Problem 3

Student Task Statement

Circle B is a dilation of Circle A.

<p>A circle with sector of a right central angle, radius 3. Unknown arc measure colored blue.</p> — Circle A

<p>A circle with sector of a right central angle, radius 9. Arc measure unknown in blue.</p> — Circle B

What is the scale factor of dilation?
What is the length of the highlighted arc in Circle A?
What is the length of the highlighted arc in Circle B?
What is the ratio of the arc lengths?
How does the ratio of arc length compare to the scale factor?

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Problem 4

ForLesson 13: Part to Whole

Student Task Statement

Kiran cuts out a square piece of paper with side length 6 inches. Mai cuts out a paper sector of a circle with radius 6 inches, and she calculates the arc length to be inches. Whose paper is larger? Explain or show your reasoning.

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Problem 5

ForLesson 13: Part to Whole

Student Task Statement

A circle has radius 3 centimeters. Suppose an arc on the circle has length centimeters. What is the measure of the central angle whose radii define the arc?

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Problem 6

ForLesson 12: Arcs and Sectors

Student Task Statement

A circle with a shaded sector is shown.

What is the area of the shaded sector?
What is the length of the arc that outlines this sector?

<p>Circle with radius 2 and highlighted sector of 50 degrees.</p>

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Problem 7

ForLesson 11: Circles in Triangles

Student Task Statement

The towns of Washington, Franklin, and Springfield are connected by straight roads. The towns wish to build an airport to be shared by all of them.

<p>Triangle FSW. Lines extend out from all vertices.</p>

Where should they build the airport if they want it to be the same distance from each town’s center? Describe how to find the precise location.
Where should they build the airport if they want it to be the same distance from each of the roads connecting the towns? Describe how to find the precise location.

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Problem 8

ForLesson 6: Inscribed Angles

Student Task Statement

Chords and intersect at point . Select all pairs of angles that must be congruent.

<p>Circle. Points A, B, C and D lie on cirlce. Chords A C and B D intersect at point E. Angles A D B, B C A, C E D and D E A.<br>
</p>

angle and angle

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Lesson 14 Resources

Student Materials

angle and angle

angle and angle

angle and angle

angle and angle