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Core Topics
- Ways of Knowing (Inductive and Deductive Reasoning)
- Introduction to Axiomatic System (Undefined Terms, Definitions, Postulates, and Theorems)
- Terminology and Classification of Geometric Objects and Shapes
- Parallelism and Perpendicularity
- Congruence
- Classical Constructions
- Concurrency (Centroid, Incenter, Circumcenter, Orthocenter, and Nine-Point Circle)
- Quadrilaterals
- Area of Polygonal Regions
- Pythagorean Theorem and Special Right Triangles
- Coordinate Geometry
- Proportional Reasoning - Similarity (Dilation)
- Introduction to Trigonometry
- Solving General Triangles and Vector Geometry (Law of Sine, Law of Cosine, Hero’s Formula)
- Circles
- Areas of Regular Polygons, Circles, and Sectors (Concept of Limits)
- Surface Areas and Volumes of Solids
Additional Topics (integrated into core topics when appropriate and as time permits)
Steiner Points (Napoleon’s Theorem)
Polyhedra - Platonic and Archimedean Solids
Transformational Geometry
Dimensions (Flatland)
Taxicab Geometry
Projective Geometry
Spherical and Hyperbolic Geometry
Textbooks:
Jacobs, Harold. Geometry – Seeing, Doing, Understanding 3rd Ed. New York: W.H. Freeman and Co., 2003. ISBN-13:978-0-71674361-3
Weeks, A. and Adkins, J. A Course in Geometry – Plane and Solid. Concord, MA: Bates Publishing Co., 1982.
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