CK12 - Geometry

Given

Reflexive

Substitution

Segmentadditionpostulate

Substitution

9. Parallellines


10. Parallelplanes


11. Parallelor perpendicularlines


12. Parallellines or segments


13. Perpendicularsegments


14. Intersectingplanes

Two-ColumnProof

LearningObjectives

• Drawa diagramto help set up a two-columnproof.


• Identifythe giveninformationand statementto be provedin a two-columnproof.


• Write a two-columnproof.

Introduction

You havedonesomeinformalproofsin earliersections.Now we raisethe levelof formalityhigher. In this
sectionyou will learnto writeformaltwo-columnproofs.You’ll needto drawa diagram,identifythe given
and prove,and writea logicalchainof statements.Eachstatementwill haveareason, suchas a definition,
postulate,or previouslyproventheorem,that justifiesit.

Given,Prove,and Diagram

Example 1

Write a two-columnprooffor the following:

If , , , and are pointson a line, in the givenorder, and , then.

Comments:The if part of the statementcontainsthe given.The then part is the sectionthat you mustprove.
A diagramshouldshowthe givenfacts.

We start with the given,prove,and a diagram.

• Given: , and are pointson a line in the ordergiven..


• Prove:.