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9-12 Geometry Unit 7 Lesson 8

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K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

Unit

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

Modeling Prompts

Lesson

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

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

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

Modeling Prompts

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

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Unit 7, Lesson 8

Arcs and Sectors

Geometry

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 7: 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 7: 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 6: 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 5: 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 2: 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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Problem 9

ForLesson 10: Cross-Sections and Volume

Student Task Statement

This solid has curved sides. All cross sections parallel to the base are squares measuring 3 units on each side. The height from the base to the top is 8 units. What is the volume of this solid?

<p>Solid with curved sides. Top and bottom bases are squares, side lengths = 3.</p>

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Lesson 8 Resources

Student Materials