Public learning track
Logical Foundations, Axioms, and Non-Euclidean Geometry
10th Grade · Math · Open Global Math
7 lessons
Goal
Analyze undefined terms, construct conditional statements and counterexamples, and compare Euclidean with spherical geometries.
Featured Diagrams
Undefined Terms: Points, Lines, Planes, and Distance
7 lessons
0 of 7 done
- 1Undefined Terms: Points, Lines, Planes, and DistanceUp nextStart
- 2Conditional Statements: Converse, Inverse, and ContrapositivePremiumNot started yet
- 3Biconditional Statements and Good Geometric DefinitionsNot started yet
- 4Deductive Reasoning: Laws of Detachment and SyllogismNot started yet
- 5Formulating Geometric Conjectures and CounterexamplesNot started yet
- 6Euclid's Postulates and the Parallel PostulateNot started yet
- 7Spherical and Hyperbolic Non-Euclidean GeometriesNot started yet
Curriculum Framework
10th Grade · Math · Open Global Math
1
7 lessons
Logical Foundations, Axioms, and Non-Euclidean Geometry
Analyze undefined terms, construct conditional statements and counterexamples, and compare Euclidean with spherical geometries.
2
8 lessons
Compass, Straightedge, and Dynamic Constructions
Perform precise classical and software-based geometric constructions and verify their theoretical foundations.
3
6 lessons
Rigid Transformations, Coordinate Mappings, and Symmetry
Represent translations, reflections, and rotations as functions on the plane and analyze symmetries and composite motions.
4
6 lessons
Transformation-Based Triangle Congruence and Proofs
Establish triangle congruence criteria using rigid transformations and write rigorous geometric proofs.
5
6 lessons
Parallel Lines, Angles, and Polygon Theorems
Prove theorems regarding lines cut by transversals, perpendicular bisectors, and interior/exterior angles of polygons.
6
6 lessons
Triangle Theorems, Concurrency, and Inequalities
Prove and apply theorems on isosceles triangles, midsegments, centers of concurrency, and triangle inequalities.
7
6 lessons
Dilations, Similarity, and Proportional Reasoning
Define similarity via dilations, establish AA, SAS, and SSS similarity criteria, and prove triangle proportionality theorems.
8
4 lessons
Right Triangle Similarity and Geometric Mean
Prove altitude-to-hypotenuse similarity theorems and use geometric mean relations to derive the Pythagorean Theorem.
9
5 lessons
Quadrilaterals: Properties, Classifications, and Proofs
Prove characterizations of parallelograms, rectangles, rhombuses, squares, and trapezoids.
10
6 lessons
Circle Theorems: Angles, Chords, and Tangents
Prove and apply theorems concerning central, inscribed, and circumscribed angles, tangent lines, and intersecting chords.
11
5 lessons
Inscribed Figures, Circumscribed Circles, and Constructions
Prove properties of cyclic quadrilaterals, construct incircles and circumcircles of triangles, and construct tangent lines.
12
6 lessons
Coordinate Geometry: Formulas, Lines, and Partitions
Derive distance, midpoint, and segment partition formulas, and write equations of parallel and perpendicular lines.
13
6 lessons
Conic Sections in Coordinate Geometry
Derive standard and general equations of circles, parabolas, ellipses, and hyperbolas using distance loci.
14
5 lessons
Coordinate Proofs and Geometric Loci
Prove geometric properties of polygons and loci algebraically using coordinate geometry.
15
5 lessons
Vector Geometry and Operations in 2D
Represent vectors geometrically and algebraically, perform vector operations, and compute magnitudes and unit vectors.
16
5 lessons
Vector Applications and Geometric Theorems
Apply vector algebra to prove classical geometric theorems and model planar geometry problems.