Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Theorems about circles
Relate chords tangents arcs and inscribed angles
Problem types
- Angles in circles
- Segment products and tangent slope in circles
- Equal radii as sides of a triangle
Builds on
- Writing and critiquing a geometric proof
- Supplementary, vertical, and adjacent angles
- Proofs about lines and angles · Useful idea
Angle relations from parallel lines and transversals are reasons in proofs of circle angle theorems.
- Angle sums and exterior angles · Useful idea
Angle sums in triangles are used to find angles in circles, such as in isosceles triangles made of two radii.
Leads to
- A tangent from a point outside a circle
- The incircle and the circumcircle
- Radians and the unit circle · Extend the idea
Central angles and arcs correspond, and radians measure a central angle as arc length divided by radius.
Related skills
- Congruence criteria for triangles · Shared foundations
- Proofs that use coordinates · Shared foundations
- Why the circle and solid formulas hold · Shared foundations
- Proofs about parallelograms · Shared foundations
- Proving triangles similar · Shared foundations
Open the interactive map to explore lessons and skill connections.