So, by the SAS postulate,thesetwo trianglesare congruent.This allowsus to find the distancebetween
Camdenand Lowellby identifyingits correspondingside on the othertriangle.Becausethey are both opposite
the verticalangle,the side connectingCamdenand Lowellcorrespondsto the side connectingMorsetown
and Grenata.Sincethe trianglesare congruent,thesecorrespondingsideswill also be congruentto each
other. Therefore,the distancebetweenCamdenand Lowellis five miles.
This use of the definitionof congruenttrianglesis one of the mostpowerfultoolsyou will use in geometry
class.It is oftenabbreviatedasCPCTC, meaningCorrespondingParts ofCongruentTrianglesareCongruent.
Constructions
Anotherimportantpart of geometryis creatinggeometricfiguresthroughconstruction.A constructionis a
drawingthat is madeusingonly a straightedgeand a compass—youcan thinkof constructionas a special
gamein geometryin whichwe makefiguresusingonly thesetools.You may be surprisedhow manyshapes
can be madethis way.
Example 4
Use a compassand straightedgeto constructthe perpendicularbisectorof the segmentbelow.Beginby usingyour compassto createan arc with the samedistancefrom a pointas the segment.