Points and : is and is. is unitsto the right and unitsbelow.Points and : is and is. is unitsto the right and unitsbelow.Points and : is and is. is unitsto the right and unitsbelow.Sincethe samerelationshipexistsbetweenthe vertices,you couldmovethe entiretriangle units
to the right and units down.It wouldexactlycovertriangle. Thesetrianglesare thereforecongruent.
SSS Postulateof TriangleCongruence
The extendedexampleaboveillustratesthat whenthreesidesof one triangleare equalin lengthto three
sidesof another, then the trianglesare congruent.We did not needto measurethe angles—thelengthsof
the correspondingsidesbeingthe same“forced”the correspondinganglesto be congruent.This leadsus
to one of the trianglecongruencepostulates:
Side-Side-Side(SSS)TriangleCongruencePostulate:If threesidesin one triangle
are congruentto the threecorrespondingsidesin anothertriangle,then the trianglesare
congruentto eachother.This is apostulateso we acceptit as true withoutproof.
You can performa quickexperimentto test this postulate.Cut two piecesof spaghetti(or a straw, or some
segment-likething)exactlythe samelength.Thencut anotherset of piecesthat are the samelengthas
eachother(but not necessarilythe samelengthas the first set). Finally, cut one morepair of piecesof
spaghettithat are identicalto eachother. Separatethe piecesinto two piles.Eachpile shouldhavethree
piecesof differentlengths.Builda trianglewith one set and leaveit on your desk.Usingthe otherpieces,
attemptto makea trianglewith a differentshapeor size by matchingthe ends.Noticethat no matterwhat
you do, you will alwaysend up with congruenttriangles(thoughthey mightbe “flippedover”or rotated).This
demonstratesthat if you can identifythreepairsof congruentsidesin two triangles,the two trianglesare
fully congruent.
Example 2
Writea trianglecongruencestatementbasedon the diagrambelow:We can see from the tick marksthat thereare threepairsof correspondingcongruentsides:, , and. Matchingup the correspondingsides,we can write the congruencestatement
.