What is a Circle?

Proving All Circles are SIMILAR

In the diagram below, you have two circles, circle A and Circle B. See if you can transform circle B so that it matches circle A exactly ("sits on" circle A). [br][br]Use the horizontal and vertical sliders to move the center of the transformation of circle B (circle B'). [br][br]Then, use the scale factor slider (sf) to adjust the radius of circle B'. [br][br]Click the double arrows in the upper right corner to reset the activity with a new pair of circles. Do this 5 times.[br][br]Then, answer the questions below the diagram.
1. Were you always able to match the circles?
2. Are circles always congruent? Explain why or why not, using your experiences in this activity.
3. Are circles always similar? Explain why or why not, using your experiences in this activity.
TRY THIS!
In our previous discussions, we talked about how to compute the scale factors between two circles that are dilated. Using the formula[math]sf=\frac{radius_{image}}{radius_{pre-image}}[/math]. Solve and answer the following questions below.
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[/img]
2. Using your knowledge about similar circles, which of the following method is [b]valid [/b]to prove that two circles are similar?

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