CK12 - Geometry

Since\angle{1}\cong\angle{2}as can applythe converseof the AlternateInteriorAnglesTheoremto

concludethat.

Noticein this examplethat you couldhavealso usedthe Converseof the CorrespondingAnglesPostulate
to provethe two linesare parallel.Also,This examplehighlightshow, if a figureis not drawnto scaleyou
cannotassumepropertiesof the objectsin the figurebasedon looks.

Converseof AlternateExteriorAngles

The moreyou practiceusingthe converseof theoremsto find solutions,the easierit will become.You have
alreadyprobablyguessedthat the converseof the AlternateExteriorAnglesTheoremis true.

Converseof the AlternateExteriorAnglesTheoremIf two linesare crossedby a

transversaland the alternateexterioranglesare congruent,then the lines crossedby the

transversalare parallel.

Puttingtogetherthe alternateexterioranglestheoremand its converse,we get the biconditionalstatement:
Two lines crossedby a transversalare parallelif and only if alternateexterioranglesare congruent.

Use the examplebelowto applythis conceptto a real-worldsituation.

Example 4

The map belowshowsthreeroadsin Julio’s town.

In Julio'stown,FranklinWay and ChavezAvenueare both crossedby Via La Playa.Julio useda surveying
tool to measuretwo anglesin the intersectionsas shownand he drewthe sketchabove(NOTto scale).
Julio wantsto knowif FranklinWay is parallelto ChavezAvenue.How can he solvethis problemand what
is the correctanswer?

Noticethat this questionasks you not only to identifythe answer, but also the processrequiredto solveit.
Makesure that your solutionis step-by-stepso that anyonereadingit can followyour logic.

To begin,noticethat the labeled angleand are alternateexteriorangles.If thesetwo anglesare
congruent,then the lines are parallel.If they are not congruent,the lines are not parallel.To find the measure

of angle , you can use the otheranglelabeledin this diagram,measuring This angleis supple-

mentaryto becausethey are a linearpair. Usingthe knowledgethat a linearpair mustbe supplementary,

find the valueof.