This chapter explains how to use reasoning to prove theorems about angle pairs and segments. This chapter also introduces the properties of congruence, which will be used in 2-column proofs.
This chapter introduces the two types of reasoning, inductive and deductive. From this foundation, rewriting statements in if-then form is discussed and then the associated forms of converse, inverse, and contrapositive are presented. Biconditional statements are explored. How to offer a conjecture and how to provide a counterexample offer beginning steps to the necessary skills needed to complete two-column proofs. The properties of equality and congruence are reviewed and practice for completing two-column proofs is provided.