How is proof developed in Discovering Geometry?
Early in the course, Discovering Geometry explains the difference between inductive reasoning—making conjectures based on observed patterns—and deductive reasoning—making logical arguments to explain these patterns. As students learn the properties of shapes, they use deductive reasoning in the form of written arguments to explain these properties. Many exercises require students to explain their thinking or to use logical deduction to justify a conjecture. After discovering triangle congruence properties, students are introduced to flowchart proofs as a means for organizing a logical argument. Later they are introduced to the two-column proof format as another method for organizing the deductive arguments of a flowchart proof. Discovering Geometry deliberately withholds the formal introduction of geometry as an axiomatic system until the culminating chapter when students have developed a deep understanding of geometric interrelationships. This chapter is particularly well suited for h
