Public learning track
Geometric Reasoning, Axiomatic Systems, and Proof Methods
9th Grade · Math · Open Global Math
7 lessons
Goal
Understand the logical architecture of geometry and construct rigorous direct proofs, indirect proofs, and counterexamples.
Featured Diagrams
Defining Points, Lines, and Line Segments
7 lessons
0 of 7 done
- 1Defining Points, Lines, and Line SegmentsUp nextStart
- 2Distinguishing Definitions, Postulates, Axioms, and TheoremsPremiumNot started yet
- 3Conditional Statements, Converses, Inverses, and BiconditionalsNot started yet
- 4Constructing Direct Synthetic ProofsNot started yet
- 5Proving Geometric Statements by ContradictionNot started yet
- 6Disproving Conjectures with CounterexamplesNot started yet
- 7Proving Triangle Properties Using Euclid's AxiomsNot started yet
Standards Covered
- OGM.10.GEO.1Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Establish geometric primitives (points, lines, planes, angles), prove angle theorems (vertical angles, complementary/supplementary angles, parallel lines cut by a transversal), and execute compass and straightedge constructions.
- 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.