# Chapter 2: Reasoning and Proof

**Basic**Created by: CK-12

## Introduction

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.

## Chapter Outline

- 2.1. Inductive Reasoning from Patterns
- 2.2. Deductive Reasoning
- 2.3. If-Then Statements
- 2.4. Converse, Inverse, and Contrapositive
- 2.5. Conjectures and Counterexamples
- 2.6. Properties of Equality and Congruence
- 2.7. Two-Column Proofs

### Chapter Summary

## Summary

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.

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## Date Created:

Feb 24, 2012## Last Modified:

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