Public learning track
Polygons, Quadrilaterals, and Midsegments
8th Grade · Math · Open Global Math
9 lessons
Goal
Prove properties of parallelograms, special quadrilaterals, trapezoids, midsegments, and calculate polygon angle sums.
Featured Diagrams
Deriving and Applying the Polygon Interior Angle Sum Formula
9 lessons
0 of 9 done
- 1Deriving and Applying the Polygon Interior Angle Sum FormulaUp nextStart
- 2Exterior Angles of Polygons: Properties and FormulaPremiumNot started yet
- 3Interior and Exterior Angles of Regular PolygonsNot started yet
- 4Properties and Proofs of ParallelogramsNot started yet
- 5Proving a Quadrilateral Is a ParallelogramNot started yet
- 6Properties and Proofs of Rectangles, Rhombuses, and SquaresNot started yet
- 7Properties and Proofs of Trapezoids and KitesNot started yet
- 8Triangle Midsegment Theorem and ProofNot started yet
- 9Trapezoid Midsegment TheoremNot started yet
Standards Covered
- OGM.9.GEO.4Open Global Math Standards 2026™ · Math · Level 9 / Grade 8 (Age 13) · Grade 8Establish, prove, and apply properties and classification of polygons and quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapezoids, mid-segment theorem, polygon interior/exterior angle sum formulas).
- 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.