Public learning track
The Pythagorean Theorem: Geometric Proofs, Converse, and Applications
9th Grade · Math · Open Global Math
7 lessons
Goal
Master geometric and similarity-based proofs of the Pythagorean theorem, use its converse to classify triangles, and solve complex multi-step geometric problems.
Featured Diagrams
The Pythagorean Theorem: Visual Proof Using Area
7 lessons
0 of 7 done
- 1The Pythagorean Theorem: Visual Proof Using AreaUp nextStart
- 2Proving the Pythagorean Theorem Using Triangle SimilarityPremiumNot started yet
- 3Using the Converse of Pythagoras' Theorem to Test Right AnglesNot started yet
- 4Classifying Acute, Right, and Obtuse Triangles Using Side LengthsNot started yet
- 5Identifying and Generating Pythagorean TriplesNot started yet
- 6Applying the Pythagorean Theorem in Three-Dimensional FiguresNot started yet
- 7Multi-Step Geometric Problems with the Pythagorean TheoremNot started yet
Curriculum Framework
9th Grade · Math · Open Global Math
1
7 lessons
The Pythagorean Theorem: Geometric Proofs, Converse, and Applications
Master geometric and similarity-based proofs of the Pythagorean theorem, use its converse to classify triangles, and solve complex multi-step geometric problems.
2
9 lessons
Foundations of Right Triangle Trigonometry
Establish sine, cosine, and tangent ratios through triangle similarity, derive exact trigonometric values for special angles, and utilize fundamental trigonometric identities.
3
7 lessons
Right Triangle Trigonometry: Solving Triangles and Real-World Applications
Solve unknown sides and angles in right triangles and apply trigonometric techniques to solve complex multi-step real-world problems.
4
5 lessons
Circle Metrics: Arc Length, Sectors, and Circular Segments
Derive and calculate arc length, sector area, and circular segment area in degrees and radians, and solve composite geometric problems.
5
10 lessons
Cavalieri's Principle and Spatial Measurement of 3D Solids
Use Cavalieri's principle and solid decomposition methods to derive and calculate surface areas and volumes of prisms, cylinders, pyramids, cones, spheres, and composite solids.
6
7 lessons
Cartographic Map Projections and Metric Distortions
Analyze how mapping a 3D spherical surface onto 2D planes induces metric distortions in angles, scale, and surface area across cylindrical, conic, and azimuthal projections.