Geometry

College

Course Outline

Course Description:

This course presents the fundamentals of plane, solid and non-Euclidean geometries. Topics include the history of mathematical thought and reasoning, measurement, congruence, similarity, parallelism, perpendicularity, and methods of proof.

 

Course Outline:

  1. Line and Angle Relationships

  2. Sets, Statements and Reasoning

  3. Informal Geometry and Measurement

  4. Early Definitions and Postulates

  5. Angles and Their Relationships

  6. Introduction to Geometric Proof

  7.   Relationships: Perpendicular Lines

  8. The Formal Proof of a Theorem

  9. Parallel Lines

  10. The Parallel Postulate and special Angles

  11. Indirect Proof

  12. Proving Lines Parallel

  13. The Angles of a Triangle

  14. Convex Polygons

  15. Triangles

  16. Congruent Triangles

  17. Corresponding Parts of Congruent Triangles

  18. Isosceles Triangles

  19. Basic Constructions Justified

  20. Inequalities in a Triangle

  21. Quadrilaterals

  22. Properties of Parallelograms

  23. The Parallelogram and Kite

  24. The Rectangle, Square, and Rhombus

  25. The Trapezoid

  26. Similar Triangles

  27. Ratios, Rates, and Proportions

  28. Similar Polygons

  29. Proving Triangles Similar

  30. The Pythagorean Theorem

  31. Special Right Triangles

  32. Segments Divided Proportionally

  33. Circles

  34. Circles and related Segments and Angles

  35. More Angle Measures in the Circle

  36. Areas of Polygons and Circles

  37. Area and Initial Postulates

  38. Perimeter and Area of Polygons

  39. Circumference and Area of a Circle

  40. Surfaces and Solids (if time permits)

  41. Prisms, Area and Volume

  42. Pyramids, Area and Volume

  43. Cylinders and Cones

  44. Polyhedrons and Spheres

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