G-C - Domain
Circles
High School Geometry · Common Core State Standards · Common Core 2010
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
circlesarrtistictheoremsrelationshipinscribed anglesradiichordscentral anglescircumscribed anglesdiameterradiustangentintersectsquadrilateralarc lengthssectorsarcradian measureconstant of proportionalityarea of a sector
Skills
- Identify (relationships among inscribed angles, radii, and chords) #dok1
- Describe (the relationship between central, inscribed, and circumscribed angles) #dok1
- Prove (that all circles are similar) #dok2
- Construct (the inscribed and circumscribed circles of a triangle) #dok2
- Derive (using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius) #dok3
- Define (the radian measure of the angle as the constant of proportionality) #dok3
- Construct (a tangent line from a point outside a given circle to the circle) #dok4
Learning Targets
- I can identify relationships among inscribed angles, radii, and chords. #dok1
- I can describe the relationship between central, inscribed, and circumscribed angles. #dok1
- I can prove that all circles are similar. #dok2
- I can construct the inscribed and circumscribed circles of a triangle. #dok2
- I can derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius. #dok3
- I can define the radian measure of the angle as the constant of proportionality. #dok3
- I can construct a tangent line from a point outside a given circle to the circle. #dok4
Big Ideas
- All circles have similar properties which can be mathematically proven.
- Understanding relationships between various circle components is crucial for geometric problem-solving.
Essential Questions
- What are the unique properties that make all circles similar?
- How do inscribed angles, radii, and chords relate to each other?
- What is the significance of radian measure in relation to circle geometry?
- In what ways can the properties of circles be applied to solve geometric problems?
- How can geometric constructions with circles be used in real-world applications?