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