A new model to use when teaching Euclidean geometry

A geometric model is introduced which satisfies the Euclidean parallel postulate as well as all of Hilbert's axioms except the Side-Angle-Side axiom. This model provides several teaching opportunities in those Euclidean geometry classrooms that use the axiomatic method. In presenting these models at the same time as the more familiar ℝ2, ℝ3, and Poincaré models, students may be less tempted to assume that familiar constructs (lines, trianges, etc.) allow them to rely on familiar assumptions.