CK12 - Geometry

NOTtrue.Thereare manyexamplesof congruentanglesthat are not verticalangles—forexamplethe
cornersof a square.

Sometimesthe converseof an if-thenstatementwill also be true. Can you think of an exampleof a statement
in whichthe converseis true?This lessonexploresconversesto the postulatesand theoremsaboutparallel
lines and transversals.

CorrespondingAnglesConverse

Let’s applythe conceptof a converseto the CorrespondingAnglesPostulate.Previouslyyou learnedthat
"if two parallellines are cut by a transversal,the correspondingangleswill be congruent."The converseof
this statementis "if correspondinganglesare congruentwhentwo linesare cut by a transversal,then the
two lines crossedby the transversalare parallel."This converseistrue, and it is a postulate.

Converseof CorrespondingAnglesPostulateIf correspondinganglesare congruent

whentwo lines are crossedby a transversal,then the two lines crossedby the transversal

are parallel.

Example 1

Supposewe knowthat and. Whatcan we concludeaboutlines and
?

Noticethat and are correspondingangles.Since , we can applythe Converseof the

CorrespondingAnglesPostulateand concludethat.

You can also use conversestatementsin combinationwith morecomplexlogicalreasoningto provewhether
lines are parallelin real life contexts.The followingexampleshowsa use of the contrapositiveof the Corre-
spondingAnglesPostulate.

Example 2

The threelines in the figurebelowrepresentmetalbars and a cablesupportinga watertower.