MAFS.912.G-C.1.1: Prove that all circles are similar. Identify and describe relationships among inscribed angles, radii, and chords.
4: I can demonstrate mathematically why all circles can be shown to be similar. I can calculate arc lengths when given a central angle size, an inscribed angle size, or a circumscribed angle size. I can calculate the area and circumference of a circle, in both decimals and in terms of pi, given either the diameter or radius. I can construct the radius of a circle, given a tangent to the circle. I can explain how a chord is related to the angle that it intersects, and also how the chord is related to the arc it cuts.
3: I can mathematically prove two or more circles similar. I can calculate arc lengths when given a central angle size, an inscribed angle size, or a circumscribed angle size. I can calculate the area and circumference of a circle, in both decimals and in terms of pi, given either the diameter or radius.I can explain how a chord is related to the angle that it intersects.
2: I can explain why all circles are similar. I can locate an inscribed angle, a circumscribed angle, a central angle, a major arc, a minor arc, and a chord. With help, I can calculate arc lengths and angle measures. I can calculate the area and circumference of a circle, in both decimals and in terms of pi, given either the diameter or radius.
1: I can explain what to do to prove that all circles are similar. I often make mistakes when trying to calculate measurements within a circle.