Public learning track
Circle Theorems: Chords, Angles, and Cyclic Quadrilaterals
9th Grade · Math · Open Global Math
7 lessons
Goal
Prove circle theorems involving chords, central and inscribed angles, angles in the same segment, and cyclic quadrilaterals.
Featured Diagrams
Perpendicular Bisector of a Chord Theorem and Proof
7 lessons
0 of 7 done
- 1Perpendicular Bisector of a Chord Theorem and ProofUp nextStart
- 2Equidistant Chords and Chords of Equal LengthPremiumNot started yet
- 3Inscribed Angle Theorem and CorollariesNot started yet
- 4Circle Theorems: Angles in the Same SegmentNot started yet
- 5Angle in a Semicircle: Thales' Circle TheoremNot started yet
- 6Circle Theorems: Cyclic QuadrilateralsNot started yet
- 7Converse: If Opposite Angles Are Supplementary, Points Lie on a CircleNot started yet
Standards Covered
- OGM.10.GEO.4Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Investigate 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™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Understand mathematical proof structure: distinguish between definitions, axioms, conjectures, theorems, and converses; construct direct synthetic proofs, proofs by contradiction (proof by contradiction), and use counterexamples.
Curriculum Framework
9th Grade · Math · Open Global Math
1
7 lessons
Geometric Reasoning, Axiomatic Systems, and Proof Methods
Understand the logical architecture of geometry and construct rigorous direct proofs, indirect proofs, and counterexamples.
2
13 lessons
Lines, Angles, and Geometric Constructions
Prove angle relationships involving intersecting and parallel lines and master classic Euclidean compass-and-straightedge constructions.
3
8 lessons
Triangle Theorems and Deductive Properties
Prove fundamental triangle theorems including angle sums, inequalities, medians, centroids, and mid-segments.
4
8 lessons
Triangle Congruence Criteria and Synthetic Proofs
Establish triangle congruence criteria (SAS, ASA, SSS, AAS, HL) and construct rigorous geometric proofs of triangle properties.
5
7 lessons
Properties and Proofs of Quadrilaterals and Polygons
Prove classification properties of special quadrilaterals, derive polygon angle sum formulas, and analyze tessellation conditions.
6
9 lessons
Similarity, Proportions, and Dilations
Prove and apply triangle similarity criteria, Thales' Theorem, area scaling laws, and explore the Golden Ratio.
7
7 lessons
Circle Theorems: Chords, Angles, and Cyclic Quadrilaterals
Prove circle theorems involving chords, central and inscribed angles, angles in the same segment, and cyclic quadrilaterals.
8
7 lessons
Tangents, Secants, and Circle Power Theorems
Prove tangent theorems, alternate segment theorem, power of a point, and execute circle tangent constructions.
9
5 lessons
Transformations, Symmetries, and Dilations in the Plane
Apply rigid motions, homothety/dilations, analyze rotational and reflectional symmetries, and calculate coordinate mappings.
10
8 lessons
Coordinate Geometry, Bearings, and Spatial Representations
Calculate coordinate distances, midpoints, slopes, navigate using three-figure bearings, and interpret 3D orthographic views and nets.