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Editor’s note: This lesson has very limited material supported by CK-12. Please refer to the Geometry Access Reader for additional materials.

Learning Objectives

  • Use similarity to generalize the results.

Similarity

We know that all circles are similar to each other.

Suppose a circle has a radius of r units.

  • The scale factor of this circle (with radius r ) and the circle with radius 1 is:

r : 1, \quad \frac{r}{1}, \quad \text{or just} \quad r.

  • You know how a scale factor affects area measures:

If the scale factor is r, then the area is r^2 times as much.

Reading Check:

1. Explain how we know that all circles are similar to each other.

(Hint: Think about similar measurements that circles may have.)

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2. If the scale factor of a circle is r, how does this relate to a circle’s area?

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Image Attributions

Description

Authors:

Grades:

8 , 9 , 10

Date Created:

Feb 23, 2012

Last Modified:

May 12, 2014
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