Geometry – mth535 (3 credits)

This course is designed to have students demonstrate the ability to use fundamental concepts of geometry including definitions, basic constructions, tools of geometry, and to recognize geometry as an axiomatic system.

This graduate-level course is 6 weeks. This course is available to take individually or as part of a degree or certificate program. To enroll, speak with an Enrollment Representative.

Foundations of Geometry, Triangles

  • Prove how triangles are congruent using geometric theorems.
  • Construct a triangle congruent to a given triangle.
  • Use congruent and right triangles to prove statements and theorems.
  • Define deductive or inductive reasoning and proofs, and axiomatic systems.
  • Identify points, lines, and planes.
  • Describe segments, rays, and angles.
  • Formulate geometric proofs.
  • Classify triangles by their sides and by their angles.

Parallel Lines and Polygons, Quadrilaterals

  • Define parallel lines, transversals, and angles.
  • Describe the characteristics of a quadrilateral.
  • Apply the properties of parallelograms.
  • Use the properties of special quadrilaterals (e.g., parallelogram, rectangles, squares, rhombus, and kite).
  • Examine the properties of trapezoids.
  • Identify different types of polygons and their components.


  • Review topics and objectives from all weeks.

Similar Polygons and the Pythagorean Theorem

  • Define ratio, proportion, and proportional segments.
  • Apply the postulates and theorems of similar polygons.
  • Construct proportional segments of polygons.
  • Demonstrate the applications of the Pythagorean Theorem.


  • Define a circle and related terms (e.g., arcs, semi-circles, inscribed angles).
  • Describe the theorems of chords and secants of circles.
  • Construct a tangent to a circle and measure angles formed by tangents.

Areas of Polygons and Circles

  • Determine areas of quadrilaterals.
  • Calculate circumference and area of circles.
  • Identify area and arc length of a sector.
  • Apply the area formula to regular polygons.

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