Course Syllabus - Honors Geometry
Note: This list represents the scope of the course but not necessarily the sequence.
Blocks: C and D Blocks
Location: Room 817
Teacher: Gary Simon
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)
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
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