🧭 Topic Guides
Deep dive into each major geometry topic with comprehensive explanations, examples, and AMC-style problems.
📚 Topic Overview
🔺 Triangle Fundamentals
- Triangles Basics - Congruence, similarity, special triangles
- Triangle Centers - Centroid, incenter, circumcenter, orthocenter
- Special Segments - Medians, altitudes, angle bisectors
📐 Angle Relationships
- Angle Chasing - Parallel lines, inscribed angles, exterior angles
- Similarity & Ratios - Dilations, angle bisector theorem, area ratios
⭕ Circle Properties
- Circles & Power of Point - Chords, tangents, secants, PoP
- Cyclic Quadrilaterals - Opposite angles, Ptolemy’s theorem
- Tangency Configurations - Incircles, excircles, tangent chains
📏 Length & Area
- Length & Area Classics - Heron, Brahmagupta, Stewart, Apollonius
🔄 Transformations & Coordinates
- Transformations - Reflections, rotations, homothety
- Coordinate Geometry - Lines, circles, shoelace formula
🎲 Advanced Topics
- Geometric Probability - Lengths, areas, random points
- 3D Geometry Light - Projections, volumes, cross-sections
- Mass Points & Ceva/Menelaus - Concurrency, collinearity
- Polygons & Tilings - Interior angles, regular polygons
- Inversion & Spiral Similarity - Advanced transformations
🎯 How to Use These Guides
Study Strategy
- Start with fundamentals - Triangles and angles are the foundation
- Build connections - See how topics relate to each other
- Practice recognition - Learn to spot common patterns
- Master techniques - Focus on problem-solving methods
Each Guide Contains
- Key concepts with clear explanations
- Micro-examples for quick understanding
- Common traps and how to avoid them
- AMC-style worked examples with full solutions
- Cross-references to related topics
Pro Tips
- Mark equalities on diagrams immediately
- Look for parallel lines - they create similar triangles
- Check for cyclicity - equal subtended angles often appear
- Use coordinate geometry when pure geometry gets messy
Next: Triangles Basics → | Back to: Geometry Mastery Guide →