Evidence of Understanding

**describe the characteristics of any circle**- construct a circle using a compass and justify that all
**radii**are**equidistant**and congruent - explain that all points on the circle are equidistant from the
**center of the circle** - define radius as a relationship between a circle’s center and
**points on the circle**- justify circles are similar using scale factor
- reason proportionally and connect the measurements of a circle with similarity

- analyze examples and non-examples to distinguish radii,
**chords**,**tangents**, and**secants** - use constructions to explain the relationship between the radius and a tangent line
- construct perpendicular bisectors of chords to show they always pass through the circle’s center

- construct a circle using a compass and justify that all
**analyze characteristics of a circle in the coordinate plane**- graph a circle in the coordinate plane given its center and radius
- explore whether a point lies on a circle whose radius and center point are known
- identify and justify possible methods including the use of a compass, straightedge, the Pythagorean Theorem, the distance formula, etc.

- prove whether a point lies on a circle given the circle’s center and another point on the circle
- describe characteristics about a circle given its center, radius, points on the circle, etc.
*Example: find the area of a circle whose endpoints of its diameter lie at (2, 3) and (10, -3), or determine the diameter of a circle centered at the origin and passing through (-5, 10)*

**determine the standard equation****of a circle in the coordinate plane**- describe connections between a circle’s
**equation**and and its graph in the coordinate plane - generate the equation of a circle from its graph
- derive the equation of a circle from the Pythagorean Theorem
- describe the relationship between
*x, h, y, k,**r*and the Pythagorean Theorem

- describe the relationship between
- generate a circle’s equation given information about its center, radius, or points on the circle
- apply completing the square to write the equation of a circle in standard form

- describe connections between a circle’s

Develop conceptual understanding:

circle, radius/radii, equidistant, center of the circle, points on the circle, equation of a circle

Supporting terms to communicate:

similar, scale factor, coordinates, Pythagorean Theorem, completing the square