Fortwotrianglestobecongruent,SAStheoremrequirestwosidesandtheincludedangleofthefirsttriangletobecongruenttothecorrespondingtwosidesandincludedangleofthesecondtriangle.Ifthecongruentanglesarenotbetweenthecorrespondingcongruentsides,thensuchtrianglescouldbedifferent.Itturnsoutthatitispossibletodescribefourcasesinwhichtrianglesarecongruenteventhoughcongruentangles.Fortwotrianglestobecongruent,SAStheoremrequirestwosidesandtheincludedangleofthefirsttriangletobecongruenttothecorrespondingtwosidesandincludedangleofthesecondtriangle.Ifthecongruentanglesarenotbetweenthecorrespondingcongruentsides,thensuchtrianglescouldbedifferent.Itturnsoutthatitispossibletodescribefourcasesinwhichtrianglesarecongruenteventhoughcongruentanglesarenotbetweenthecorrespondingcongruentsides.Suchatheoremcouldbenamed,forexample,SSAtheorem.ManytextsstatethattwotrianglescannotbeshowntobecongruentiftheconditionofSSAexists.However,theauthordescribescasesinwhichsuchtrianglescouldbeprovencongruentwiththeSSAtheorem.Animmediateconsequenceofthisnewunderstandingisthenecessityofrevisingmanyproblemsandanswersinhighschoolandcollege-leveltextsrelatedtocongruenttriangles.arenotbetweenthecorrespondingcongruentsides.Suchatheoremcouldbenamed,forexample,SSAtheorem.Animmediateconsequenceofthisnewunderstandingisthenecessityofrevisingmanyproblemsandanswersinhighschoolandcollege-leveltextsrelatedtocongruenttriangles.
