CK12 - Geometry

AlternateInteriorAnglesTheoremAlternateinterioranglesformedby two parallellines

and a transversalwill alwaysbe congruent.

•

Given: and are parallellines crossedby transversal

• Provethat AlternateInteriorAnglesare congruent

Note:It is sufficientto provethat one pair of alternateinterioranglesare congruent.Let'sfocuson proving

.

Statement Reason

1.Given

1.

2. 
   
   
   
   2. CorrespondingAnglesPostulate
   
   
   
   


3. 
   
   
   
   3. VerticalAnglesTheorem
   
   
   
   


4. 
   
   
   
   4. Transitivepropertyof congruence
   
   
   
   

AlternateExteriorAnglesTheorem

Now you knowthat pairsof corresponding,vertical,and alternateinterioranglesare congruent.We will use
logicto showthat AlternateExteriorAnglesare congruent—whentwo parallellinesare crossedby a
transversal,of course.

Example 4

Lines and in the diagrambeloware parallel.If , whatis the measureof?

You knowfrom the problemthat. That meansthat ’s correspondingangle,whichis

, will measure as well.