Unit 13: Circles and Spheres

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Essential Questions: 
  • What figures are always similar to each other?
  • How are circles and Pythagorean Theorem related?
  • Why are we still using triangles with circles?
  • What does a circle become in three dimensions? What are the similarities and differences between that object and a circle?
Content: 
  • Definition of a circle.
  • Representation of a circle on a coordinate plane - equation.
  • Coordinate proofs for: angle inscribed in a semicircle is right, line through center of circle and midpoint of chord is perpendicular to the chord, distances between congruent chords and the center of the circle are equal.
  • When can't we use coordinate proofs?
  • Intersection of circles and lines.
  • Using similarity theorems to prove circle theorems.
  • Comparing circles to spheres.
  • Surface area and volume of a sphere.
Skills and Processes: 
  • Generate equation of a circle using distance formula.
  • Write equation of a circle given center and radius.
  • Write equation of a circle given a center and a point on the radius.
  • Proving circle theorems with and without coordinate proofs.
  • Solving systems of circles and lines.
  • Calculate volume and surface area of spheres.