Public learning track
Triangle Theorems, Inequalities, and Centers
8th Grade · Math · Open Global Math
12 lessons
Goal
Prove core triangle theorems, evaluate triangle inequalities, and analyze medians, altitudes, angle bisectors, perpendicular bisectors, and triangle centers.
Featured Diagrams
Classifying Triangles: Equilateral, Isosceles, Scalene, and Right-Angled
12 lessons
0 of 12 done
- 1Classifying Triangles: Equilateral, Isosceles, Scalene, and Right-AngledUp nextStart
- 2Proving the Triangle Angle Sum TheoremPremiumNot started yet
- 3Finding Missing Angles Using the Exterior Angle TheoremNot started yet
- 4Base Angles Theorem: Isosceles Triangle PropertiesNot started yet
- 5Equilateral and Equiangular Triangle CorollariesNot started yet
- 6The Triangle Inequality: Why Some Side Lengths FailNot started yet
- 7Applying the Triangle Inequality Theorem to Solve ProblemsNot started yet
- 8Side-Angle Inequality Relationships in TrianglesNot started yet
- 9Medians and the Centroid TheoremNot started yet
- 10Altitudes and the OrthocenterNot started yet
- 11Perpendicular Bisectors and the CircumcenterNot started yet
- 12Angle Bisectors and the IncenterNot started yet
Standards Covered
- 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.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.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).
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.