Foundations in Geometry
Revised: August 2007
Axiomatic approach to the study and development of Euclidean and non-Euclidean geometry. Prerequisite: Junior standing or permission of Department Head.
At the conclusion of this course, the successful student will demonstrate
1. knowledge of the synthetic, investigative, and deductive approaches to Euclidean plane geometry.
2. knowledge of the historical and mathematical significance of the parallel postulate, including an introduction to a non-Euclidean geometry.
3. proficiency in the basic concepts of mathematical logic and their use in proofs.
Goldman Berele. Geometry: Theorems and Constructions, Pearson-Prentice Hall, 2001.
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Notation and Conventions (1 day)
Basic terms; standard notation; construction vs. drawing
- Congruent Triangles (2 weeks)
Fundamental ideas of geometric proof; triangle congruence theorems; special triangles; applications to constructional applications to inequalities
Parallel Lines (2 weeks)
Existence and uniqueness; applications; distance between parallel lines
Area (1 week)
Area formulas for triangles and quadrilaterals; Pythagorean Theorem; decomposition
Similar Triangles (1 week)
Basic theorems; applications to constructions
Circles (2 weeks)
Circles and tangents; arcs and angles; applications to constructions
Regular Polygons (1 week)
Constructability; basic theorems
More on Triangles and Circles (4 weeks)
Circumcircles; inscribed circles; classic circle problems; medians; altitudes; special points; Euler Line; Nine-Point Circle; classic triangle problems
Supplement (2 weeks)
Platonic solids, Euclidean and projective transformations and constructions using classical tools and computer software