- 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?
- 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.