Example 5
List all pairsof alternateanglesin the diagrambelow.Thereare two typesof alternateangles—alternateinterioranglesand alternateexteriorangles.As you
needto list themboth,beginwith the alternateinteriorangles.
Alternateinterioranglesare on the interiorregionof the two lines crossedby the transversal,so that wouldincludeangles and Alternateanglesare on oppositesidesof the transversal,. So, the two
pairsof alternateinterioranglesare & , and and.
Alternateexterioranglesare on the exteriorregionof the two lines crossedby the transversal,so that wouldincludeangles and Alternateanglesare on oppositesidesof the transversal,. So, the two
pairsof alternateexterioranglesare & , and and.
LessonSummary
In this lesson,we exploredhow to workwith differenttypesof lines,anglesand planes.Specifically, we
havelearned:
- How to identifyparallellines,skewlines,and parallelplanes.
- How to identifyand use the ParallelLine Postulate.
- How to identifyand use the PerpendicularLine Postulate.
- How to identifyanglesand transversalsof manytypes.
Thesewill help you solvemanydifferenttypesof problems.Alwaysbe on the lookoutfor new and interesting
waysto examinethe relationshipbetweenlines,planes,and angles.
Pointsto Consider
Parallelplanesare two planesthat do not intersect.Parallellinesmustbe in the sameplaneand they do
not intersect.If morethan two lines intersectat the samepointand they are perpendicular, then they cannot
be in sameplane(e.g.,the , , and axesare all perpendicular).However, if just two lines are
perpendicular, then thereis a planethat containsthosetwo lines.
As you moveon in your studiesof paralleland perpendicularlines you will usuallybe workingin one plane.
This is oftenassumedin geometryproblems.However, you mustbe carefulaboutinstanceswhereyou are
workingwith multipleplanesin space.Generallyin three-dimensionalspaceparalleland perpendicularlines
are morechallengingto workwith.
LessonExercises
Solveeachproblem.