Name: ____________________________________ 13-9 Notes and Practice

Geometry PD. __________ Date: _________

Today’s Goal: How do you prove all circles are similar through transformations?

Think back to when we proved figures were similar. Our proofs looked like

this:

Using your knowledge from above, try this:

1. Using a sequence of transformations, prove that circle A of radius 3 and circle C of radius 8 are similar.

Proving Circles are Similar

* To prove any two circles are similar, only a _________________ (slide) and ______________ (enlargement or reduction) are necessary.

*If not clear in a diagram, exact translations can be determined using the differences in the ________________ coordinates

*Use radii to determine the scale factor. Remember:

One more for you to try

2.

Prove that circle C with center (–1, 2) and radius 3 is similar to circle D with center (3, 4) radius 1.

ATTENTION: When you are proving on the coordinate

plane, you can be more precise!

3. Harry Potter is proving that the two circles below are similar. He completed the translation so that the centers are coinciding. Complete the next step of this proof.

4. Show the two given circles are similar by stating the necessary transformations from C to D.

C: center (2, 3) radius 5; D: center (–1, 4) radius 10.

5. Consider the two circles graphed below. Show that they are similar by stating the necessary transformations from A to C. (no conclusion necessary here)!

Name: ________________________________________ 13-9 HomeworkGeometry Per. ______ Date: ________

Complete each problem. Be sure to check the key tonight.

1. Show the two given circles are similar by thoroughly describing the necessary transformations from C to D.

C: center (–2, 8) radius 2; D: center (0, 4) radius 9.

2. Using transformations, prove that circle U is similar to circle A by mapping circle U onto circle A. Use specific details.

3. In the accompanying diagram, is tangent to circle O at A. Radii and are drawn, and is

extended to intersect at B. If and , find the measure of a radius of circle O.

4.

5. In the diagram below, is a tangent to circle O at point S, is a secant, , , and . Find PR .