CK12 - Geometry

Given and are crossedby and.

Prove

Statement Reason

1. Given


2. and are crossedby and
   .


3. 
   
   
   
   2. VerticalAnglesTheorem
   
   
   
   


4. 
   
   
   
   3. TransitivePropertyof AngleCongruence
   
   
   
   


5. Converseof the CorrespondingAngles


6. Postulate.

Noticein the proofthat we had to showthat the correspondingangleswerecongruent.Oncewe had done
that, we satisfiedthe conditionsof the Converseof the CorrespondingAnglespostulate,and we coulduse
that in the final step to provethat the lines are parallel.

Example 3

Are the two lines in this figureparallel?

This figureshowstwo lines that are cut by a transversal.We don'tknow. However, if you look at its

linearpair, that anglehas a measureof By the LinearPair Postulate,this angleis supplementaryto

. In otherwords,the sum of and will be Use subtractionto find.

So,. Now look and. is a verticalanglewith the anglemeasuring By the Vertical

AnglesTheorem,.