This course will examine concepts in Euclidean and non-Euclidean geometries. Course topics include: area and volume, congruence and similarity, properties of and relationships among geometric shapes and structures. The Pythagorean Theorem, and motion and symmetry. Students will engage with these concepts through proofs, problem solving, dynamic geometric software, and through activities used in middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.