CK12 - Geometry

• Alternateinteriorangles:Theseanglesare on the interiorof the lines crossedby the transversaland are
  on oppositesidesof the transversal.Thereare two pairsof alternateinterioranglesin this diagram—
  and , and and.


• Alternateexteriorangles:Theseare on the exteriorof the linescrossedby the transversaland are on

oppositesidesof the transversal.Thereare two pairsof alternateexterioranglesin this diagram—

and , and and.

• Consecutiveinteriorangles:Consecutiveinterioranglesare in the interiorregionof the lines crossedby
  the transversal,and are on the sameside of the transversal.Thereare two pairsof consecutiveinterior
  anglesin this diagram— and and and.

CorrespondingAnglesPostulate

By now you havehad lots of practiceand shouldbe able to easilyidentifyrelationshipsbetweenangles.

CorrespondingAnglesPostulate:If the linescrossedby a transversalare parallel,then corresponding
angleswill be congruent.Examinethe followingdiagram.

You alreadyknowthat and are correspondinganglesbecausethey are formedby two lines crossed
by a transversaland havethe samerelativeplacementnext to the transversal.The CorrespondingAngles
postulatesays thatbecausethe lines are parallelto eachother,the correspondingangleswill be congruent.

Example 2

In the diagrambelow, lines and are parallel.Whatis the measureof?

Becauselines and are parallel,the angleand are correspondingangles,we knowby the

CorrespondingAnglesPostulatethat they are congruent.Therefore,.

AlternateInteriorAnglesTheorem

Now that you knowthe CorrespondingAnglesPostulate,you can use it to derivethe relationshipsbetween
all otheranglesformedwhentwo lines are crossedby a transversal.Examinethe anglesformedbelow.