Lesson 1 CCSS Understand and apply theorems about circles.

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Presentation transcript:

Lesson 1 CCSS Understand and apply theorems about circles. Prove that all circles are similar.

Given: Circle C with center C and radius r Given: Circle C with center C and radius r. Circle D with center D and radius s.

Prove: Circle C is similar to circle D.

Ti Nspire or Geogebra construction 1. Transform circle C with a translation with vector CD. 2. Through this …….., the image of point C is …. 3. Let the image of circle C be circle C’, the center of circle C’ coincide with point …… 4. Transform circle C' with a Dilation and with a factor of s/r. 5. Circle C' is made up of all the points at distance ......... from point .......

After the dilation, the image of circle C’ will consist of all the points at distance …….. from point D. These are the same points that form circle …….. Therefore, the ……. followed by the dilation maps circle C to circle …… Because …….. and dilations are …….. you can conclude that circle C is …. to circle …..

After the dilation, the image of circle C’ will consist of all the points at distance …s….. from point D. These are the same points that form circle …C’….. Therefore, …translation…. followed by the dilation maps circle C to circle …C’… Because …translation….. and dilations are …transformation….. you can conclude that circle C is …similar... to circle …C’..

Reflections Can you show that circle C and D are similar through another sequence of similarity transformations? Explain. Is it possible that circle C and circle D are congruent? If so, does the proof of the similarity of the circles still work? Explain.

Assignment Answer the following questions about the dartboard shown above. l. Are the circles similar? Explain, using the concept of a dilation in your explanation' 2. You throw a dart and it sticks in a random location on the board. What is the probability that it sticks in circle A? circle B? circle C? circle D? Explain how you found your answers.