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## Similarity of Circles

#### Circles - HSG-C.A.1

What is Similarity of Circles? When we talk about similarity in geometry, it refers to a property where at least two shapes are relative to each other. When to shapes are said to be similar, they possess the same properties in the same proportion to one another. In the context of similarity, proportionality directs to all the values being multiples of each other within a given question. We know that circles are defined by two main properties, the center and radius. Remember that similarity does not depend on positions; hence, the similarity if circles depend mainly on radii of circles. We also know that radius is a constant and unchanging number, and that every constant is proportional to another constant. So, keeping this in mind, all circles must be similar! Remember congruence? Congruent shapes are identical, just like identical twins! They have the same size, angles, proportions. Congruence, like similarity, is also independent of position, rotation and reflection. By definition, all congruent shapes are similar, but not every similar shape is congruent. This selection of worksheets and lessons help students use the fact that all circles are similar as a tool to predict translations and scaling procedures.

### Printable Worksheets And Lessons  #### Homework Sheets

Follow the dilation of a circle across a coordinate system.

• Homework 1 - After translating the center of F to the center of F', dilate F about its new center to contract F' onto F.
• Homework 2 - How did this all come about?
• Homework 3 - You can use notation to state the translation and the scale factor.

#### Practice Worksheets

I made these really big so that you could see them closely and go over them step by step.

• Practice 1 - You can transform circle F to circle F' by translating it and then performing a dilation. Find the translation rule and the scale factor of the dilation.
• Practice 2 - See if you can forecast how these movements came about.
• Practice 3 - To find the scale factor of this dilation, calculate the radio of the radii.