# Chapter 2: Reasoning and Proof

Difficulty Level:

**Basic**Created by: CK-12Turn In

## 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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Description

This chapter gives students an introduction to the concepts surrounding proofs. Included topics are inductive reasoning, conditional statements, and properties of congruence.

Difficulty Level:

Basic
Tags:

angle pairs
biconditional statements
CK.MAT.ENG.SE.1.CK-12-Concept-Basic-Geometry.2
(18 more)
conclusion
conditional statements
congruence
conjecture
contrapositive
converse
counterexamples
deductive reasoning
hypothesis
if-then statement
inductive reasoning
inverse
Law of Contrapositive
Law of Detachment
Law of Syllogism
logic
patterns
proof

Subjects:

Date Created:

Feb 24, 2012
Last Modified:

Jun 09, 2016
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