Public learning track
Logic, Definitions, and Geometric Proof Methods
8th Grade · Math · Open Global Math
7 lessons
Goal
Understand axiomatic structures, formulate conditional statements and converses, identify counterexamples, and construct direct and indirect geometric proofs.
Featured Diagrams
Undefined Terms: Points, Lines, Planes, and Axioms
7 lessons
0 of 7 done
- 1Undefined Terms: Points, Lines, Planes, and AxiomsUp nextStart
- 2Conditional Statements: Hypotheses and ConclusionsPremiumNot started yet
- 3Converse, Inverse, Contrapositive, and BiconditionalsNot started yet
- 4Counterexamples and Disproving ConjecturesNot started yet
- 5Two-Column Proofs and Deductive Reasoning ChainsNot started yet
- 6Paragraph and Flowchart Proof FormatsNot started yet
- 7Indirect Proof and Proof by ContradictionNot started yet
Standards Covered
- OGM.9.GEO.1Open Global Math Standards 2026™ · Math · Level 9 / Grade 8 (Age 13) · Grade 8Understand and apply geometric axiomatic facts and definitions (points, lines, planes, segments, angles, perpendiculars, transversals); solve problems using angle relationships (supplementary, complementary, vertically opposite, alternate interior, corresponding, interior consecutive angles).
- OGM.9.GEO.6Open Global Math Standards 2026™ · Math · Level 9 / Grade 8 (Age 13) · Grade 8Understand logical proof structures (definitions, propositions, converse, direct proof, proof by contradiction, counterexamples) and construct rigorous synthetic geometric proofs.
Curriculum Framework
8th Grade · Math · Open Global Math
1
7 lessons
Logic, Definitions, and Geometric Proof Methods
Understand axiomatic structures, formulate conditional statements and converses, identify counterexamples, and construct direct and indirect geometric proofs.
2
9 lessons
Angle Relationships and Parallel Line Proofs
Calculate unknown angle measures and formally prove parallel line properties and their converses.
3
12 lessons
Triangle Theorems, Inequalities, and Centers
Prove core triangle theorems, evaluate triangle inequalities, and analyze medians, altitudes, angle bisectors, perpendicular bisectors, and triangle centers.
4
9 lessons
Triangle Congruence Criteria and Proofs
Master and prove the triangle congruence postulates (SSS, SAS, ASA, AAS, HL) and construct rigorous multi-step geometric proofs.
5
9 lessons
Polygons, Quadrilaterals, and Midsegments
Prove properties of parallelograms, special quadrilaterals, trapezoids, midsegments, and calculate polygon angle sums.
6
11 lessons
Compass-and-Straightedge Geometric Constructions
Execute classic compass-and-straightedge constructions and construct formal geometric proofs justifying why each construction works.
7
9 lessons
Circle Theorems, Tangents, and Inscribed Angles
Prove and apply theorems regarding central angles, inscribed angles, chords, tangent lines, and cyclic quadrilaterals.
8
9 lessons
Pythagorean Theorem, 3D Applications, and Coordinate Distance
Prove the Pythagorean Theorem and its converse, apply it to 2D and 3D figures, and derive the coordinate distance formula.