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9-12 Integrated Math 2 Unit 7 Lesson 12

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K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 •Integrated Math 2 Integrated Math 3

Unit

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

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
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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 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
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Lesson 12
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Lesson 17
Lesson 18

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Unit 7, Lesson 12

Arcs and Sectors

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Integrated Math 2

Practice

Problem 1
Student Task Statement
Suppose a circle is divided into congruent slices. Match each number of slices with the resulting central angle measure of each slice.

2

3

4

5

6

8

45
60
72
120
90
180

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Problem 2

Student Task Statement

A circle of radius 12 units is divided into 8 congruent slices.

What is the area of each slice?
What is the arc length of each slice?

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Problem 3

Student Task Statement

Diego says, “To find arc length, divide the measure of the central angle by 360. Then multiply that by the area of the circle.“ Do you agree with Diego? Show or explain your reasoning.

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Problem 4

ForLesson 11: Circles in Triangles

Student Task Statement

The image shows a triangle.

<p>Triangle A B C.</p>

Sketch the inscribed and circumscribed circles for this triangle.
Compare and contrast the two circles.

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Problem 5

ForLesson 11: Circles in Triangles

Student Task Statement

Triangle is shown with its inscribed circle drawn. The measure of angle is 72 degrees. What is the measure of angle ? Explain or show your reasoning.

<p>Triangle A B C with inscribed circle, center G. Point E is on B C. Point F is on A C. E G and F G are radii. Angle A C B is 72 degrees.</p>

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Problem 6

ForLesson 10: A Special Point

Student Task Statement

How do the values of and compare? Explain your reasoning.

<p>Quadrilateral A E D F with line A D bisecting angle A into two 35 degree angles and creating 2 triangles, A D E and A D F.</p> — ;

;

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Problem 7

ForLesson 9: Triangles in Circles

Student Task Statement

Points and are the corners of a triangular park. The park district is going to add a set of swings inside the park. The goal is to have the swings equidistant from the vertices of the park. Find a location that meets this goal. Explain or show your reasoning.

<p>Point A, B, and C.</p>

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Problem 8

ForLesson 6: Inscribed Angles

Student Task Statement

In the diagram, the measure of the arc from to not passing through is 80 degrees. What is the measure of angle ?

<p>Irregular quadrilateral A O B C inscribed in circle with center O. O B and O A are radii.</p>

20 degrees
40 degrees
80 degrees
160 degrees

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Lesson 12 Resources

Student Materials