lesson
Circle Theorems: Cyclic Quadrilaterals
Prove that the opposite angles of a cyclic quadrilateral are supplementary (sum to 180 degrees).
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This lesson is part of a track
Public learning track
Circle Theorems: Chords, Angles, and Cyclic Quadrilaterals
7 lessons
Goal
Prove circle theorems involving chords, central and inscribed angles, angles in the same segment, and cyclic quadrilaterals.
7 lessons
0 of 7 done
- Perpendicular Bisector of a Chord Theorem and ProofUp next
- Equidistant Chords and Chords of Equal LengthNot started yet
- Inscribed Angle Theorem and CorollariesNot started yet
- Circle Theorems: Angles in the Same SegmentNot started yet
- Angle in a Semicircle: Thales' Circle TheoremNot started yet
- Circle Theorems: Cyclic QuadrilateralsYou are here
- Converse: If Opposite Angles Are Supplementary, Points Lie on a CircleNot started yet
Learning standards covered
OGM.10.GEO.4Open Global Math Standards 2026™ · 9th GradeInvestigate and prove circle theorems: perpendicular bisector of a chord, inscribed angle theorem and its corollaries, cyclic quadrilaterals, tangents and secants, and tangent segment lengths from an external point.
OGM.10.GEO.5Open Global Math Standards 2026™ · 9th GradeUnderstand mathematical proof structure: distinguish between definitions, axioms, conjectures, theorems, and converses; construct direct synthetic proofs, proofs by contradiction (proof by contradiction), and use counterexamples.