MATH 456 - Geometry for Teachers

• Demonstrate an understanding of the axiomatic structure of geometry, including definitions, axioms and theorems and will reason using the language and structure of geometry, both orally and in writing.
• Make conjectures based on inductive reasoning and justify and prove those conjectures using deductive reasoning based on the axiomatic structure of Euclidean geometry.
• Establish congruence and similarity criteria and use them to prove congruence and similarity of polygonal figures.  Students will recognize and use proportional relationships within similar figures to solve problems.
• Investigate the connections between the traditional approach to geometry and a modern approach using transformational geometry.  Students will perform reflection, rotation, translation and dilation in the plane using traditional construction tools as well as using analytic formulas requiring the use of coordinate geometry and matrix and vector operations.
• Use appropriate dynamical geometry software to investigate and represent concepts, methods and application of geometry.
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems.