She drew , and made.
Thenshe carefullydrew , making and =.
At this point,Cherylhad drawntwo segments( and ) with lengthsthat are proportionalto the
lengthsof the correspondingsidesof , and she had madethe includedangle, , congruent
to the includedangle( ) in.
ThenCherylmeasuredangles.She foundthat:
•
WhatcouldCherylconclude?Hereagainwe haveautomaticresults.The otheranglesare automatically
congruent,and the trianglesare similarby AAA or AA. Cheryl’s worksupportsthe SAS for SimilarTriangles
Postulate.
SimilarTrianglesSummary
We’ve exploredsimilartrianglesextensivelyin severallessons.Let’s summarizethe conditionswe’vefound
that guaranteethat two trianglesare similar.
Two trianglesaresimilarif and only if:
- the anglesin the trianglesare congruent.
- the lengthsof correspondingsidesin the polygonsare proportional.
AAA::If the anglesof a triangleare congruentto the correspondinganglesof anothertriangle,then the tri-
anglesare similar.
AA::It two pairsof correspondinganglesin two trianglesare congruent,then the trianglesare similar.
SSS for SimilarTriangles:If the lengthsof the sidesof two trianglesare proportional,then the triangles
are similar.
SASfor SimilarTriangles:If the lengthsof two correspondingsidesof two trianglesare proportionaland
the includedanglesare congruent,then the trianglesare similar.
Pointsto Consider
Haveyou evermadea modelrocket?Haveyou seena scaledrawing?Do you knowpeoplewho use
blueprints?Do you enlargepictureson your computeror shrinkthem?Theseare all examplesof similar
two-dimensionalor three-dimensionalobjects.
LessonExercises
Triangle1 has sideswith lengths inches, inches,and inches.
Triangle2 has sideswith lengths feet, feet, and feet.
- Are Triangle1 and Triangle2 congruent?Explainyour answer.
- Are Triangle1 and Triangle2 similar?Explainyour answer.