COLLEGE GEOMETRY I

Prerequisites & course information

Requisites: MATH 234 or ( MATH 222 and COMP SCI/MATH 240 ) or MATH 375 or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program Course Designation: Core GenEd - Natural Science & Wellness + Lab Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Spring 2026 Learning Outcomes: 1. Recall and state the formal definitions of mathematical objects and their properties used in axiomatic and coordinate geometry with a special emphasis on triangles and circles (e.g., pedal triangles, Simson line, perpendicular bisector, etc.). Audience: Undergraduate 2. Use the above definitions to argue if a mathematical construct does or does not have the condition of having a particular property (e.g., that two triangles are congruent, three points are collinear, etc.). Audience: Undergraduate 3. Recall and state standard theorems used in axiomatic geometry including their proofs (e.g., opposite angles are congruent, Ceva's Theorem, nine-point circle theorem, etc.). Audience: Undergraduate 4. Verify the premises of standard theorems in in order to apply their conclusions in the context of longer arguments (e.g., arguing congruence by verifying angle sums, etc.). Audience: Undergraduate 5. Prove or disprove statements related to the definitions, properties, and theorems of axiomatic geometry using the techniques of mathematical argument. In particular, the student will employ construction and computational techniques as necessary. Audience: Undergraduate 6. Convey formal mathematical arguments in written and/or verbal English using appropriate mathematical terminology and notation. Audience: Undergraduate Learning Outcomes: 1. Recall and state the formal definitions of mathematical objects and their properties used in axiomatic and coordinate geometry with a special emphasis on triangles and circles (e.g., pedal triangles, Simson line, perpendicular bisector, etc.). Audience: Undergraduate 2. Use the above definitions to argue if a mathematical construct does or does not have the condition of having a particular property (e.g., that two triangles are congruent, three points are collinear, etc.). Audience: Undergraduate 3. Recall and state standard theorems used in axiomatic geometry including their proofs (e.g., opposite angles are congruent, Ceva's Theorem, nine-point circle theorem, etc.). Audience: Undergraduate 4. Verify the premises of standard theorems in in order to apply their conclusions in the context of longer arguments (e.g., arguing congruence by verifying angle sums, etc.). Audience: Undergraduate 5. Prove or disprove statements related to the definitions, properties, and theorems of axiomatic geometry using the techniques of mathematical argument. In particular, the student will employ construction and computational techniques as necessary. Audience: Undergraduate 6. Convey formal mathematical arguments in written and/or verbal English using appropriate mathematical terminology and notation. Audience: Undergraduate