Unit 4.4 Deriving the Equation of a Circle and Proving that all Circles are Similar Instructional Days: 9.

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Unit 4.4 Deriving the Equation of a Circle and Proving that all Circles are Similar Instructional Days: 9

Common Core Standards Expressing Geometric Properties with Equations G-GPE Translate between the geometric description and the equation for a conic section G-GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Use coordinates to prove simple geometric theorems algebraically [Include distance formula; relate to Pythagorean theorem] G-GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). Circles G-C Understand and apply theorems about circles G-C.1 Prove that all circles are similar.

Standards of Math Practice SMP 1 Make sense of problems and persevere in solving them Derive the equation of a circle Use completing the square to write the equation of a circle in standard form SMP 3 Construct viable arguments and critique the reasoning of others Prove all circles are similar Explain how to find the equation of a circle SMP 7 Look for and make use of structure Make a connection between the Pythagorean Theorem and the equation of a circle Understand the connection between factoring and completing the square

Essential Questions What is the purpose of completing the square? Why are all circles similar? Why can we use the Pythagorean Theorem to derive the equation of a circle?