Foundations of Geometry


This chapter establishes the foundational building blocks of Euclidean geometry, including a brief review of sets. The undefined terms are introduced, as well as defined terms and the first postulates and theorems. Linear and angular measures are introduced, as well as terminology relating to two- and three-dimensional figures. You will also learn to differentiate among sketches, drawings, and constructions.

What you can expect to learn

After completing these activities you should be able to

  1. Express relationships between sets and perform set operations.
  2. Describe the structure and characteristics of an ideal geometric system.
  3. Apply foundational definitions, postulates, and theorems.
  4. Identify subsets of lines and planes.
  5. Measure segments and angles.
  6. Idenify and name circles, polygons, and related terms.
  7. Calculate the perimeter of a polygon and the circumference of a circle.
  8. Identify and name spheres, cones, cylinders, and polyhedra, included prisms and pyramids.
  9. Create accurate sketches and drawings.
  10. Construct congruent segments and angles.
  11. Recognize that a person's worldview affects every area of life, including mathematics. 
Activity List