Lookat this diagramcarefullyto establishthe relationshipbetweenlines and and lines and.Startingwith line , the angleshownmeasures This angleis an alternateexteriorangleto the
anglelabeledon line. Sincethe alternateexterioranglesare congruent,thesetwo lines are parallel.Next
look at the relationshipbetween and. The angleshownon line measures and it corresponds
to the anglemarkedon line. Sincethe correspondingangleson thesetwo lines are congruent,lines
and are also parallel.Usingthe ParallelLinesProperty, we can identifythat lines and are parallel,because is parallelto
and is also parallelto.Note that thereare manyotherwaysto reasonthroughthis problem.Can you think of one or two alternative
waysto show?
LessonSummary
In this lesson,we exploredhow to workwith the converseof theoremswe alreadyknew. Specifically, we
havelearned:
- How to identifyand use the CorrespondingAnglesConversePostulate.
- How to identifyand use the Converseof AlternateInteriorAnglesTheorem.
- How to identifyand use the Converseof AlternateExteriorAnglesTheorem.
- How to identifyand use the Converseof ConsecutiveInteriorAnglesTheorem.
- How to identifyand use the ParallelLinesProperty.
Thesewill help you solvemanydifferenttypesof problems.Alwaysbe on the lookoutfor new and interesting
waysto applytheoremsand postulatesto mathematicalsituations.
PointsTo Consider
You havenow studiedthe manyrulesaboutparallellines and the anglesthey form.In the next lesson,you
will delvedeeperinto conceptsof lines in the -plane.You will applysomeof the geometricproperties
of lines to slopesand graphingin the coordinateplane.
LessonExercises
Solveeachproblem.
- Are lines and parallelin the diagrambelow?If yes, how do you know?