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and. Are the lines and parallel?To find out whetherlines and are parallel,you mustidentifythe correspondinganglesand see if theyare congruent.In this diagram, and are correspondinganglesbecausethey are formedby the
transversaland the two lines crossedby the transversaland they are in the samerelativeplace.
The problemstatesthat and. Thus,they are not congruent.If thosetwo
anglesare not congruent,the linesare not parallel.In this scenario,the lines and (andthus the
supportbars they represent)are NOTparallel.
Notethat just becausetwo linesmay look parallelin the picturethat is not enoughinformationto say that
the lines are parallel.To provetwo lines are parallelyou needto look at the anglesformedby a transversal.
AlternateInteriorAnglesConverse
Anotherimportanttheoremyou derivedin the last lessonwas that whenparallel linesare cut by a
transversal,the alternateinterioranglesformedwill be congruent.The converseof this theoremis, "If alternate
interioranglesformedby two lines crossedby a transversalare congruent,then the lines are parallel."This
statementis also true, and it can be provenusingthe Converseof the CorrespondingAnglesPostulate.
Converseof Alternate Interior Angles Theorem If two lines are crossed by a
transversaland alternateinterioranglesare congruent,then the lines are parallel.