This text was designed for an IBL approach to Introduction to Geometries and coverc geometry topics required for secondary teacher certification. As a result it covers synthetic, transformational, and a tiny bit of analytic approaches to geometry and covers both Euclidean (parabolic), hyperbolic, and some projective geometry. Students are expected to have completed a proofs course covering proof techniques, basic set operations, and cardinality as a prerequisite. The students have typically taken high school geometry.
Thumbnail: 2-sphere wireframe as an orthogonal projection. (CC BY-SA 3.0; Geek3 via Wikipedia)