Public learning track
Compass-and-Straightedge Geometric Constructions
8th Grade · Math · Open Global Math
11 lessons
Goal
Execute classic compass-and-straightedge constructions and construct formal geometric proofs justifying why each construction works.
Featured Diagrams
Copying Segments and Angles with Compass and Straightedge
11 lessons
0 of 11 done
- 1Copying Segments and Angles with Compass and StraightedgeUp nextStart
- 2Constructing Perpendicular Bisectors and MidpointsPremiumNot started yet
- 3Constructing Angle BisectorsNot started yet
- 4Constructing Perpendicular Lines Through a Point on or off a LineNot started yet
- 5Constructing Parallel Lines Through a Given PointNot started yet
- 6Constructing Triangles from Given SSS, SAS, and ASA ConditionsNot started yet
- 7Constructing Equilateral Triangles and Regular HexagonsNot started yet
- 8Constructing Squares and Inscribed Regular PolygonsNot started yet
- 9Constructing Inscribed and Circumscribed Circles of TrianglesNot started yet
- 10Constructing Tangent Lines to a Circle from an External PointNot started yet
- 11Using Constructions to Prove Geometric PropertiesNot started yet
Standards Covered
- OGM.9.GEO.7Open Global Math Standards 2026™ · Math · Level 9 / Grade 8 (Age 13) · Grade 8Execute compass-and-straightedge geometric constructions (angle bisector, perpendicular bisector, copying angles, parallel lines, triangles from given elements, inscribed/circumscribed circles, regular polygons, circle tangents).
- OGM.9.GEO.5Open Global Math Standards 2026™ · Math · Level 9 / Grade 8 (Age 13) · Grade 8Understand and apply the properties of circles (central angles, inscribed angles, chords, perpendicular chord theorem, tangent lines, tangent segments theorem, inscribed/circumscribed polygons, incenter, circumcenter).
- 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.