Angles, Arcs, and Radii

ID: dagik-gunil
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
Standards: HSG-C.B.5HSG-C.A.1HSG-GMD.A.1HSG-SRT.A.1.b
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8 questions

Angles, Arcs, and Radii

Classroom:
Due:
Student Name:
Date Submitted:
Comparing Progress

Han and Tyler are each completing the same set of tasks on an online homework site. Han is using his smartphone and Tyler is using his tablet computer. Their progress is indicated by the circular bars shown in the image. The shaded arc represents the tasks that have been completed. When the full circumference of the circle is shaded, they will be finished with all the tasks.

A template for answering this question. Ask your instructor for an alternative.

1) Tyler says, “The arc length on my progress bar measures 4.75 centimeters. The arc length on Han’s progress bar measures 2.25 centimeters. So, I’ve completed more tasks than Han has.”


Is Tyler correct?

True or false? Write below.

2) Explain your reasoning.

3) What information would you need to make a completely accurate comparison between the two students’ progress?

A Dilated Circle

The image shows 2 circles. The second circle is a dilation of the first circle using a scale factor of 3.

For each part of the dilated image, determine the factor by which it’s changed when compared to the corresponding part of the original circle.

A template for answering this question. Ask your instructor for an alternative.

4) the area of the sector

a)

The scale factor is 9.

b)

The scale factor is 3

c)

The scale factor is 1, which means

that this part of the dilated image

does not change.

5) the central angle of the sector

a)

The scale factor is 9.

b)

The scale factor is 3

c)

The scale factor is 1, which means

that this part of the dilated image

does not change.

6) the radius

a)

The scale factor is 9.

b)

The scale factor is 3

c)

The scale factor is 1, which means

that this part of the dilated image

does not change.

7) the length of the arc defined by the sector

a)

The scale factor is 9.

b)

The scale factor is 3

c)

The scale factor is 1, which means

that this part of the dilated image

does not change.

8) the ratio of the circle's circumference to its diameter

a)

The scale factor is 9.

b)

The scale factor is 3

c)

The scale factor is 1, which means

that this part of the dilated image

does not change.