Evidence of Understanding

**describe proportional relationships between angles, arcs, and sectors of a circle**- create visuals to describe a
**central angle**in terms of the fraction of the circle it represents*Example: show an angle measuring 72° is equivalent to ⅕ of the circle*

- investigate the constant ratio between an angle’s
**arc length**and a circle’s**circumference******explain the proportional relationship with the radius- use similarity to derive the length of the arc intercepted by an angle
- use tools to verify the relationship between an angle’s
**degree**and**radian**measure

- apply the relationship between degrees and radians to find a missing measure
- determine and justify the length of 1 radian

- explain how
**sectors**are related to area of a circle using similarity relationships- derive and use the formula for determining the area of a sector

- derive and use the formula for determining the area of a sector

- create visuals to describe a
**analyze and apply the relationships****between the angles and arcs used to describe a circle**- use examples and nonexamples to distinguish central,
**inscribed,**and**circumscribed angles**- define and classify angles using radii, chords, and tangents

- investigate relationships between angle and arc measure for a central, inscribed, or circumscribed angle and use them to solve problems
- prove inscribed angles open to the same arc are congruent (and vice versa)
- prove parallel chordsintercept congruent arcs

- prove that a triangle inscribed in a circle with a leg through the center of the circle is a right triangle (hypotenuse is the diameter)
- describe patterns relating the angle and arc measures on a circle by two tangents, two secants, a secant and a tangent, or a chord and a tangent
- describe patterns relating the angle and arc measures resulting from two intersecting chords
- calculate the value of an unknown angle or arc measure

- use examples and nonexamples to distinguish central,

Develop conceptual understanding:

central angle, arc length, circumference, degrees, radians, sector, inscribed angle, circumscribed angle

Supporting terms to communicate:

equivalent, ratio, proportion, similarity, scale factor, dilation, angle, radius, diameter, area, chord, tangent, secant, parallel, alternate interior angles, hypotenuse