Public learning track
Pythagorean Theorem, 3D Applications, and Coordinate Distance
8th Grade · Math · Open Global Math
9 lessons
Goal
Prove the Pythagorean Theorem and its converse, apply it to 2D and 3D figures, and derive the coordinate distance formula.
Featured Diagrams
Geometric Dissection Proofs of the Pythagorean Theorem
9 lessons
0 of 9 done
- 1Geometric Dissection Proofs of the Pythagorean TheoremUp nextStart
- 2Deriving the Pythagorean Theorem Using Similar TrianglesPremiumNot started yet
- 3Proving and Applying the Converse of the Pythagorean TheoremNot started yet
- 4Classifying Acute, Right, and Obtuse Triangles Using Side LengthsNot started yet
- 5Solving Multi-Step 2D Problems with the Pythagorean TheoremNot started yet
- 6Applying the Pythagorean Theorem in 3D Space and PrismsNot started yet
- 7Deriving the Distance Formula from the Pythagorean TheoremNot started yet
- 8Finding Distance Between Two Points Using PythagorasNot started yet
- 9Verifying Segment Congruence Using the Distance FormulaNot started yet
Standards Covered
- OGM.9.GEO.8Open Global Math Standards 2026™ · Math · Level 9 / Grade 8 (Age 13) · Grade 8Explain and prove the Pythagorean Theorem and its converse using algebraic and geometric models; apply it to calculate unknown side lengths in 2D/3D figures and find the Euclidean distance between points in coordinate space.
- 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.
- OGM.9.GEO.2Open Global Math Standards 2026™ · Math · Level 9 / Grade 8 (Age 13) · Grade 8Establish and prove triangle properties (interior angle sum theorem = 180°, exterior angle theorem, triangle inequality, medians, altitudes, centroid, perpendicular bisector, angle bisector) and classify isosceles, equilateral, and right triangles.
- OGM.9.GEO.3Open Global Math Standards 2026™ · Math · Level 9 / Grade 8 (Age 13) · Grade 8Establish and prove criteria for triangle congruence (SAS, ASA, SSS, AAS, HL) and design deductive algorithms/steps to verify congruence between geometric figures.
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.