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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,r1,or justr
.

  • You know how a scale factor affects area measures:

If the scale factor is r, then the area is r2 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.)

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

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