Historically, educators have held up the study of Euclidean geometry as a model of learning deductive reasoning rooted in axioms. However, axioms based solely on the Elements may not get a high school student all the way to clean, rigorous proofs of congruence and similarity from a transformation approach. While Euclid did allude to superposition by isometries, he did not axiomatize this idea. In this talk, I will discuss an axiomatic system for College Geometry that satisfies the following properties: (1) The system supports proofs of congruence and similarity of all polygons as well as curves defined as a locus of points such as conic sections; (2) it has the potential, with minimal modification, be suitable for use with high school students; (3) it treats angles in a way that generalize easily to angle usage in trigonometry and precalculus. This system combines and adapts Wu’s (2013) and Picciotto and Douglas’s (2017) systems.


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