CK12 - Geometry

8. [Diff: 2]


9. [Diff: 2]


10. [Diff: 2]


11. Proofof ConsecutiveInteriorAngleTheorem.Given , prove and are supplementary.

Statement Reason

1.

Given

1. s


2. 
   
   
   
   2. CorrespondingAnglesPostulate
   
   
   
   


3. and are supplementary3. LinearPair Postulate


4. 
   
   
   
   4. Definitionof supplementaryangles
   
   
   
   


5. 
   
   
   
   5. Substitution( )
   
   
   
   


6. and are supplementary6. Definitionof supplementaryangles

ProvingLinesParallel

LearningObjectives

• Identifyand use the Converseof the CorrespondingAnglesPostulate.


• Identifyand use the Converseof AlternateInteriorAnglesTheorem.


• Identifyand use the Converseof AlternateExteriorAnglesTheorem.


• Identifyand use the Converseof ConsecutiveInteriorAnglesTheorem.


• Identifyand use the ParallelLinesProperty.

Introduction

If two anglesare verticalangles,then they are congruent.You learnedthis as the VerticalAnglesTheorem.
Can you reversethis statement?Can you swapthe “if” and “then”partsand will the statementstill be true?

Theconverseof a logicalstatementis madeby reversingthe hypothesisand the conclusionin an if-then
statement.Withthe VerticalAnglesTheorem,the converseis “If two anglesare congruentthen they are
verticalangles.”Is that a true statement?In this case,no. The converseof the VerticalAnglesTheoremis