Proving Circles Similar by Transformations
Proving Circles are Similar
In this sketch we will take the definition of similar to mean that a figure can be translated, rotated, reflected, and dilated in order to map one figure exactly to another figure.
In this applet, you can attempt to translate and dilate to see if you can get one circle to match up completely with the other circle. If you can, the circles are similar.
First, use the horizontal and vertical sliders to translate circle B' on the plane.
Next, use the scale factor slider to adjust the radius of circle B'.
Can you translate and dilate circle B' and get it to match up with circle A? If so, the circles are similar.
Click the arrows in the upper right corner to reset the activity with a new pair of circles.