CK12 - Geometry

Angle is equalto This angleis widerthan the otheralternateexteriorangle,which

measures so the alternateexterioranglesare not congruent.Therefore,FranklinWay and Chavez
Avenueare not parallelstreets.

In this example,we usedthe contrapositiveof the converseof the AlternateExteriorAnglesTheoremto
provethat the two lines werenot parallel.

Converseof ConsecutiveInteriorAngles

The final conversetheoremto explorein this lessonaddressedthe ConsecutiveInteriorAnglesTheorem.
Rememberthat theseanglesaren’tcongruentwhenlinesare parallel,they are supplementary. In other
words,if the two linesare parallel,the angleson the interiorand on the sameside of the transversalwill

sum to So, if two consecutiveinterioranglesmadeby two linesand a transversaladd up to
the two lines that form the consecutiveanglesare parallel.

Example 5

Identifywhetherlines and in the diagrambeloware parallel.

Usingthe converseof the ConsecutiveInteriorAnglesTheorem,you shouldbe able to identifythat if the

two anglesin the figureare supplementary, then lines and are parallel.We add the two consecutive
interioranglesto find their sum.

?

The two anglesin the figuresum to so lines and are in fact parallel.

ParallelLinesProperty

The last theoremto explorein this lessonis calledthe ParallelLinesProperty. It is a transitiveproperty.
Doesthe phrasetransitivepropertysoundfamiliar?You haveprobablystudiedothertransitiveproperties
before,but usuallytalkingaboutnumbers.Examinethe statementbelow.

If and , then

Noticethat we useda propertysimilarto the transitivepropertyin a proofabove.The ParallelLinesProperty

says that if line is parallelto line , and line is parallelto line , then lines and are also par-
allel. Use this informationto solvethe final practiceproblemin this lesson.

Example 6

Are lines and in the diagrambelowparallel?