CK12 - Geometry

Whatis

Sinceyou knowthat line is perpendicularto line , you can fill in the four right anglesat that inter-
section.

The anglethat correspondsto is a right angle. This is true becauseyou knowlines and

are parallel. Thus,the correspondinganglesmustbe congruent.So is a right angle.It

measures

Noticein this examplethat if is a right angle,then all of the anglesformedby the intersectionof

lines and are right angles.Lines and are perpendicularas well. This is a resultof the
CorrespondingAnglesPostulate.

As in previousproblemsinvolvingparallellinescrossedby a transversal,all pairsof anglesremaineither
congruentor supplementary. Whendealingwith perpendicularlines,however, all of the anglesare right
angles.

ConverseTheoremwith PerpendicularTransversals

Whenexaminingthe scenarioof a perpendiculartransversalwith parallellines,a conversetheoremcan be
applied.The conversestatementsays that if a transversalformsright angleson two differentcoplanarlines,
thosetwo linesare parallel.Thinkbackto the conversetheoremsyou studiedearlierin this chapter. They
statedthat if correspondingangleswerecongruent,consecutiveinterioranglesweresupplementary, or
otherspecificrelationship,then the two lines wereparallel.Use this conversetheoremto understanddifferent
graphicsituations.

Example 2

Line belowis a transversal,cuttingthroughlines and.