Chapter 2: Reasoning and Proof
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.
 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 Keywords
 Inductive Reasoning
 Conjecture
 Counterexample
 Conditional Statement (IfThen Statement)
 Hypothesis
 Conclusion
 Converse
 Inverse
 Contrapositive
 Biconditional Statement
 Logic
 Deductive Reasoning
 Law of Detachment
 Law of Contrapositive
 Law of Syllogism
 Right Angle Theorem
 Same Angle Supplements Theorem
 Same Angle Complements Theorem
 Reflexive Property of Equality
 Symmetric Property of Equality
 Transitive Property of Equality
 Substitution Property of Equality
 Addition Property of Equality
 Subtraction Property of Equality
 Multiplication Property of Equality
 Division Property of Equality
 Distributive Property
 Reflexive Property
 of Congruence
 Symmetric Property
 of Congruence
 Transitive Property of Congruence
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, 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.