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Unit 4.4  Deriving  the Equation of a Circle and Proving that all Circles are Similar Unit 4.4  Deriving  the Equation of a Circle and Proving that all Circles are Similar

Unit 4.4 Deriving the Equation of a Circle and Proving that all Circles are Similar - PowerPoint Presentation

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Unit 4.4 Deriving the Equation of a Circle and Proving that all Circles are Similar - PPT Presentation

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

circle equation prove circles equation circle circles prove geometric pythagorean similar theorem square theorems smp completing gpe derive find

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Presentation Transcript

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?