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Geometry and Spatial Reasoning

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📊 Overall Study Progress

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📐 Geometry Fundamentals

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Master the foundational building blocks of geometry including points, lines, planes, angles, and basic shapes

  • Khan Academy: Basic Geometry and Measurement: Comprehensive introduction to geometry fundamentals with interactive exercises covering points, lines, angles, and basic shapes Khan Academy Basic Geometry
    📝 Notes
  • Kevin's Guides: Fundamental Geometry Concepts: 2024 tutorial covering all the basics including segments, rays, planes, angles, postulates, and theorems Geometry Basics Guide
    📝 Notes
  • Virtual Nerd: Fundamentals of Geometry: Video tutorials on fundamental geometry concepts with visual demonstrations and step-by-step explanations Virtual Nerd Geometry
    📝 Notes
  • Online Math Learning: Basic Geometry Concepts: Comprehensive lessons with diagrams, examples, and step-by-step solutions for basic geometry Basic Geometry Concepts
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🧠 Spatial Reasoning and Visualization

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Develop spatial visualization skills through mental rotation, 3D thinking, and visual-spatial problem solving

📜 Euclidean Geometry and Proofs

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Master classical Euclidean geometry including axioms, postulates, theorems, and formal proof techniques

  • Euclid's Elements Interactive Edition: Complete interactive text of all 13 Books with dynamic diagrams and comprehensive explanations Euclid's Elements Interactive Edition
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  • Byrne's Euclid: Colorful Interactive Elements: Beautifully designed 1847 edition with interactive diagrams, cross-references, and color-coded proofs Byrne's Euclid: Colorful Interactive Elements
    📝 Notes
  • UGA: Introduction to Proofs in Euclidean Geometry: Academic guide to classical proofs including triangle theorems and inscribed angles UGA: Introduction to Proofs in Euclidean Geometry
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  • Vaia: Euclidean Geometry Principles: Learn Euclidean geometry axioms, theorems, and proof techniques with modern explanations Vaia: Euclidean Geometry Principles
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📊 Coordinate and Analytic Geometry

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Apply algebraic methods to geometric problems using coordinate systems, distance formulas, and analytical techniques

🔄 Geometric Transformations

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Understand and apply translations, rotations, reflections, and dilations to geometric figures

📐 Trigonometry and Right Triangles

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Master trigonometric ratios, identities, and their applications in geometry and real-world problems

  • Khan Academy: Trigonometry: Complete trigonometry course from basics to advanced applications with practice exercises Khan Academy: Trigonometry
    📝 Notes
  • Khan Academy: Applications of Trigonometry: Real-world applications including heights, distances, and architectural problems Khan Academy: Applications of Trigonometry
    📝 Notes
  • Govst: Trigonometry Short Course: Comprehensive PDF tutorial covering all essential trigonometry concepts Govst: Trigonometry Short Course
    📝 Notes
  • Algonquin College: Geometry & Trigonometry Guide: Study guide combining geometry and trigonometry concepts for college-level mathematics Algonquin College: Geometry & Trigonometry Guide
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⭕ Circle Geometry

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Explore circle theorems, arc and chord properties, tangent lines, and inscribed angles

🧊 3D Geometry and Solid Shapes

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Understand three-dimensional shapes, polyhedra, surface area, volume, and spatial relationships

  • Math is Fun: Solid Geometry: Complete guide to 3D geometry covering common solids, polyhedra, volume, and surface area Math is Fun: Solid Geometry
    📝 Notes
  • Khan Academy: Nets of Polyhedra: Video introduction to understanding how 2D nets fold into 3D polyhedra Khan Academy: Nets of Polyhedra
    📝 Notes
  • Fluxspace: Paper Polyhedra Construction: Hands-on STEAM activity for constructing polyhedra and exploring 3D geometry Fluxspace: Paper Polyhedra Construction
    📝 Notes
  • Subject Coach: Vertices, Edges and Faces: Tutorial on polyhedra properties including Euler's formula and volume calculations Subject Coach: Vertices, Edges and Faces
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➡️ Vectors in Geometry

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Apply vector concepts including dot product, cross product, and vector operations to geometric problems

  • GeeksforGeeks: Dot and Cross Products: Comprehensive guide to vector operations with geometric interpretations and applications GeeksforGeeks: Dot and Cross Products
    📝 Notes
  • Khan Academy: Cross Products: Interactive lessons on cross products in multivariable calculus with visual examples Khan Academy: Cross Products
    📝 Notes
  • Better Explained: Understanding the Cross Product: Intuitive explanation of cross products with geometric visualization and real applications Better Explained: Understanding the Cross Product
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  • Math LibreTexts: The Dot and Cross Product: Academic textbook treatment of vector products with proofs and applications Math LibreTexts: The Dot and Cross Product
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🌐 Non-Euclidean Geometry

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Explore hyperbolic and spherical geometries beyond Euclidean space and understand curved surfaces

🎯 Advanced Geometry Topics

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Explore advanced concepts including projective geometry, fractal geometry, and geometric constructions

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