This course is required for Secondary Education students specializing in math. It is also taken by math majors who are interested in geometry or who want to gain experience in writing proofs before they attempt more advanced math courses.
In this course students learn to understand and to write proofs of geometric facts. Also, they gain an appreciation of some of the more beautiful and amazing theorems of Euclidean geometry. The course begins with a thorough review of high-school geometry and continues with a selection of more advanced topics.
The precise content of the course varies, but some of the topics that are often covered are
- Review of high-school geometry
- Special points of triangle.
- The nine-point circle.
- Simson lines.
- The theorems of Ceva and Menelaus.
- Morley's theorem.
- Vectors techniques of proof.
- Radical axes of circles.
- Compass and straightedge constructions.