Public learning track
Triangle Theorems, Angles, and Inequalities
7th Grade · Math · Open Global Math
7 lessons
Goal
Apply interior and exterior angle theorems, side-angle relationships, and the triangle inequality to classify and solve triangles.
Featured Diagrams
Triangle Angle Sum Theorem: Proof and Applications
7 lessons
0 of 7 done
- 1Triangle Angle Sum Theorem: Proof and ApplicationsUp nextStart
- 2Exterior Angle Theorem of TrianglesPremiumNot started yet
- 3Solving Algebraic Equations with Triangle AnglesNot started yet
- 4Base Angles Theorem: Isosceles Triangle PropertiesNot started yet
- 5Equilateral and Equiangular Triangle PropertiesNot started yet
- 6Applying the Triangle Inequality Theorem to Solve ProblemsNot started yet
- 7Relationships Between Side Lengths and Opposite Angles in TrianglesNot started yet
Standards Covered
- OGM.8.GEO.2Open Global Math Standards 2026™ · Math · Level 8 / Grade 7 (Age 12) · Grade 7Investigate, prove, and apply theorems about triangles: interior angle sum theorem (180°), exterior angle theorem, triangle inequality theorem, congruence criteria (SSS, SAS, ASA, AAS, HL), isosceles/equilateral properties, right triangles, and the Pythagorean theorem.
- OGM.8.GEO.6Open Global Math Standards 2026™ · Math · Level 8 / Grade 7 (Age 12) · Grade 7Understand deductive reasoning, definitions, conditional propositions, converse statements, theorems, and proof techniques including direct synthetic proof, counterexamples, and proof by contradiction.
Curriculum Framework
7th Grade · Math · Open Global Math
1
9 lessons
Angle Relationships and Parallel Lines
Identify and calculate unknown angles using complementary, supplementary, vertical, and parallel line transversal relationships with algebraic equations.
2
7 lessons
Triangle Theorems, Angles, and Inequalities
Apply interior and exterior angle theorems, side-angle relationships, and the triangle inequality to classify and solve triangles.
3
7 lessons
Triangle Congruence Criteria and Proofs
Prove triangles congruent using SSS, SAS, ASA, AAS, and HL criteria and deduce corresponding parts.
4
9 lessons
The Pythagorean Theorem and Right Triangle Geometry
Prove, calculate, and apply the Pythagorean theorem and its converse to 2D and 3D real-world problems.
5
7 lessons
Quadrilaterals, Polygons, and Angle Sums
Classify quadrilaterals, prove polygon properties, and calculate interior and exterior angle sums of n-sided polygons.
6
8 lessons
Deductive Reasoning, Logic, and Geometric Proofs
Construct direct proofs, converse statements, counterexamples, and proofs by contradiction to establish geometric truths.
7
9 lessons
Circle Foundations, Pi, Circumference, and Arcs
Define pi, calculate circumference and arc length, and analyze chords, tangents, and central and inscribed angles.
8
7 lessons
Area of Circles, Sectors, and Composite 2D Shapes
Derive circle area, calculate sector and segment areas, and solve perimeter and area for composite plane figures.
9
9 lessons
Geometric Constructions and Loci
Execute precise geometric constructions using compass, straightedge, protractor, and dynamic geometry software.
10
7 lessons
Rigid Transformations and Symmetry in the Plane
Perform and describe translations, reflections, and rotations on and off the coordinate plane and identify symmetries.
11
9 lessons
Dilations, Similarity, and Scale Drawings
Apply dilations, establish triangle similarity criteria (AA, SAS, SSS), and solve scale drawing and perimeter/area ratio problems.
12
6 lessons
Introduction to Right Triangle Trigonometry
Define sine, cosine, and tangent ratios, compute exact values for 30°, 45°, 60°, and solve right triangles.
13
7 lessons
3D Visualization: Orthographic Views, Nets, and Cross-Sections
Represent 3D objects with front/top/side orthographic projections, nets, isometric drawings, and plane cross-sections.
14
8 lessons
Surface Area and Volume of 3D Solids
Calculate lateral surface area, total surface area, and volume of prisms, pyramids, cylinders, and composite solids, modeling volume relationships.