CK-12 Geometry-Concepts

http://www.ck12.org Chapter 2. Reasoning and Proof

TABLE2.26:(continued)

Statement Reason

2.m^6 ACH=m^6 ECH 2.

3. 
   
   
   
   3. Angle Addition Postulate
   
   
   
   


4. 
   
   
   
   4. Substitution
      5.m^6 ACE= 2 m^6 ACH 5.
   
   
   
   


5. 
   
   
   
   6. Division PoE
   
   
   
   


6. 
   
   
   
   7. 
      
   
   
   
   

Summary

This chapter teaches students how to make conjectures and provide counterexamples. From there, it focuses on
rewriting statements in if-then 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 two-column proofs is provided.

Symbol Toolbox for Chapter

→if-then

∧and

∴therefore

∼not

∨or

Chapter Keywords

• Inductive Reasoning


• Conjecture


• Counterexample


• Conditional Statement (If-Then 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