Instructional Days 9 Common Core Standards Expressing Geometric Properties with Equations GGPE Translate between the geometric description and the equation for a conic section GGPE1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem complete the squ ID: 627522
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Slide1
Unit 4.4 Deriving the Equation of a Circle and Proving that all Circles are Similar
Instructional Days: 9Slide2
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.Slide3
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 squareSlide4
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?