Introduction
This chapter explains how to reason and how to use reasoning to prove theorems about angle pairs and segments. This chapter also introduces the properties of congruence, which will also be used in proofs. Subsequent chapters will combine what you have learned in Chapters 1 and 2 and build upon them.
Chapter Outline
 2.1. Conjectures and Counterexamples
 2.2. IfThen Statements
 2.3. Converse, Inverse, and Contrapositive
 2.4. Inductive Reasoning from Patterns
 2.5. Deductive Reasoning
 2.6. Truth Tables
 2.7. Properties of Equality and Congruence
 2.8. TwoColumn Proofs
Chapter Summary
Summary
This chapter teaches students how to make conjectures and provide counterexamples. From there, it focuses on rewriting statements in ifthen form and finding converses, inverses, and contrapositives. Two types of reasoning, inductive and deductive, are explored. Finally, the properties of equality and congruence are reviewed and practice for completing twocolumn proofs is provided.
Symbol Toolbox for Chapter
Chapter Review
Match the definition or description with the correct word.

5=x andy+4=x , then5=y+4 — A. Law of Contrapositive  An educated guess — B. Inductive Reasoning

6(2a+1)=12a+12 — C. Inverse  2, 4, 8, 16, 32,... — D. Transitive Property of Equality

AB¯¯¯¯¯≅CD¯¯¯¯¯ andCD¯¯¯¯¯≅AB¯¯¯¯¯ — E. Counterexample 
∼p→∼q — F. Conjecture  Conclusions drawn from facts. — G. Deductive Reasoning
 If I study, I will get an “
A ” on the test. I did not get anA . Therefore, I didn’t study. — H. Distributive Property 
∠A and∠B are right angles, therefore∠A≅∠B . — I. Symmetric Property of Congruence  2 disproves the statement: “All prime numbers are odd.” — J. Right Angle Theorem — K. Definition of Right Angles
Texas Instruments Resources
In the CK12 Texas Instruments Geometry FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9687.
Image Attributions
Description
Difficulty Level:
At GradeTags:
Subjects:
Date Created:
Jul 17, 2012Last Modified:
Feb 26, 2015If you would like to associate files with this chapter, please make a copy first.