Concept Taxonomy
This taxonomy organizes the 200 geometry concepts into 12 categories for better navigation and understanding.
Categories
1. Foundation Concepts (FOUND)
TaxonomyID: FOUND
Description: The most fundamental building blocks of geometry including undefined terms (point, line, plane) and basic geometric objects. These concepts have minimal or no dependencies.
Examples: Point, Line, Plane, Ray, Line Segment, Angle
2. Logic and Reasoning (LOGIC)
TaxonomyID: LOGIC
Description: Concepts related to mathematical reasoning, proof techniques, and logical argumentation used throughout geometry.
Examples: Inductive Reasoning, Deductive Reasoning, Conditional Statement, Proof, Theorem
3. Angle Relationships (ANGLE)
TaxonomyID: ANGLE
Description: Classifications of angles and relationships between angles, including complementary, supplementary, and angles formed by transversals.
Examples: Acute Angle, Complementary Angles, Vertical Angles, Corresponding Angles
4. Constructions (CONST)
TaxonomyID: CONST
Description: Compass and straightedge construction techniques used to create geometric figures.
Examples: Compass Construction, Copying a Segment, Bisecting an Angle, Constructing Perpendiculars
5. Transformations (TRANS)
TaxonomyID: TRANS
Description: Geometric transformations including translations, rotations, reflections, dilations, and their compositions.
Examples: Translation, Rotation, Reflection, Rigid Motion, Congruent Figures
6. Lines and Planes (LINES)
TaxonomyID: LINES
Description: Relationships between lines, including parallel and perpendicular lines, and coordinate geometry of lines.
Examples: Parallel Lines, Perpendicular Lines, Transversal, Slope, Equations of Lines
7. Triangles (TRI)
TaxonomyID: TRI
Description: Triangle classifications, properties, congruence criteria, special segments, and centers.
Examples: Triangle, Isosceles Triangle, Triangle Congruence, SSS Congruence, Centroid
8. Polygons (POLY)
TaxonomyID: POLY
Description: Multi-sided figures including quadrilaterals, regular polygons, and their properties.
Examples: Polygon, Quadrilateral, Parallelogram, Rectangle, Pentagon, Tessellation
9. Similarity and Right Triangles (SIM)
TaxonomyID: SIM
Description: Similar figures, proportional reasoning, Pythagorean theorem, and trigonometric ratios.
Examples: Similar Figures, Scale Factor, Pythagorean Theorem, Sine Ratio, Indirect Measurement
10. Circles (CIRC)
TaxonomyID: CIRC
Description: Parts of circles, angles and arcs in circles, and equations of circles.
Examples: Circle, Radius, Chord, Tangent, Central Angle, Arc Length, Equation of Circle
11. Area and Volume (AREA)
TaxonomyID: AREA
Description: Formulas and concepts for calculating area of 2D figures, perimeter, circumference, surface area, and volume of 3D solids.
Examples: Area of Triangle, Circumference, Volume of Prism, Surface Area, Cavalieri's Principle
12. Applications (APP)
TaxonomyID: APP
Description: Real-world applications of geometry including modeling, design, optimization, and capstone projects.
Examples: Scale Drawing, Modeling with Geometry, Optimization Problem, Design Challenge
Distribution Guidelines
- Foundation Concepts: ~10 concepts
- Logic and Reasoning: ~20 concepts
- Angle Relationships: ~15 concepts
- Constructions: ~8 concepts
- Transformations: ~12 concepts
- Lines and Planes: ~15 concepts
- Triangles: ~30 concepts
- Polygons: ~20 concepts
- Similarity and Right Triangles: ~20 concepts
- Circles: ~20 concepts
- Area and Volume: ~25 concepts
- Applications: ~5 concepts
Total: 200 concepts