Mathematics 135

Math 135

Fundamentals of Geometry

Catalog Entry

MATH 135. Fundamentals of Geometry
Three Lecture hours (3).

Prerequisites: Mathematics major or permission of the instructor.

Introduces core concepts and principles of Euclidean geometry, with some attention also given to non-Euclidean geometry. Emphases are placed on the use of spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties from both formal and informal perspectives. Course content adheres to the National Council of Teachers of Mathematics Standards (2000) and the Virginia Standards of Learning where they can appropriately be applied. Students who have earned credit for MATH 109 may not subsequently earn credit for MATH 135.


Detailed Description of Course

Course content includes:

  • Axiomatic Based Geometry:
  • Axiomatic Systems
  • Parallel and Perpendicular Lines
  • Triangles and Similar triangles
  • Polygons
  • Circles
  • Measurement:
  • Area
  • Perimeter
  • Volume
  • Trigonometric relationships
  • Transformational Geometry
  • Translations
  • Rotations
  • Reflections – Symmetry
  • Special Topics
  • Fractals
  • Tessellations


Description of Conduct of Course

Course instructors will model the type of instruction they encourage students to use as future teachers. Instruction will include cooperative/group learning and projects, student presentations, small group and whole class discussions and questioning, and student explorations of geometric concepts using manipulatives and technology. Diverse assessments will be used, including formative assessments where students monitor their own learning and this information helps guide instructional decisions.


Student Goals and Objectives of the Course

Course content and design emphasizes the NCTM Standards for mathematics education and other research-based instructional strategies. The primary goal is to prepare students for effective classroom teaching of geometry and related problem-solving strategies in secondary grades by helping them to think critically and creatively about ideas, issues, problems, and texts both within and across academic disciplines. This will happen through problem solving, writing direct and indirect geometric proofs, conjecture, construction of visualizations (e.g., using computers or physical models), and individual and group mathematical investigations in a shared process of inquiry and problem-solving. Students will deepen their understandings of the connections among course concepts, procedures, and applications while also developing proficiency with geometric skills including constructing logical and persuasive arguments. Students will develop their understanding of axiomatic reasoning and the role it has played in the development of mathematics.


Assessment Measures

Graded tasks may include homework, quizzes, and written exams. They may also include writing assignments, self or peer assessments, individual or group projects or presentations, and class participation.


Other Course Information


Review and Approval Date