NY Next Generation Math GEO-G.C.2.a

MathGrades 9–12Understand and apply theorems about circles.

The Standard

Identify, describe and apply relationships between the angles and their intercepted arcs of a circle.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students identify and apply relationships between angles and intercepted arcs in circles. They use central, inscribed, and related angle measures to solve problems and support proofs.
What Mastery Looks Like: The student marks the correct intercepted arc and writes a valid angle-arc relationship. The student can use the relationship to prove a result such as supplementary opposite angles in an inscribed quadrilateral.
Common Misconceptions: Students may use the wrong arc or double an angle that should be halved. They may apply an inscribed-angle rule when the vertex is not on the circle.
How to Assess It: Give a circle diagram with a central angle, an inscribed angle, and one unknown arc. Ask students to solve and name each relationship used.

Lesson moves

Measure inscribed angles on paper circles and compare each with its intercepted arc using string.
Ask why two inscribed angles intercepting the same arc must be congruent.
Play angle-arc match with diagrams, measures, and relationship statements.
Use a circular track or wheel diagram to locate sight angles and intercepted arcs.

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