- Classifytrianglesas scalene,isosceles,or equilateral.
Introduction
By this point,you shouldbe able to readilyidentifymanydifferenttypesof geometricobjects.You have
learnedaboutlines,segments,rays,planes,as well as basicrelationshipsbetweenmanyof thesefigures.
Everythingyou havelearnedup to this pointis necessaryto explorethe classificationsand propertiesof
differenttypesof shapes.The next two sectionsfocuson two-dimensionalshapes—shapesthat lie in one
plane.As you learnaboutpolygons,use whatyou knowaboutmeasurementand anglerelationshipsin
thesesections.
DefiningTriangles
The first shapeto examineis thetriangle.Thoughyou haveprobablyheardof trianglesbefore,it is helpful
to reviewthe formaldefinition.A triangleis any closedfiguremadeby threeline segmentsintersectingat
their endpoints.Everytrianglehas threevertices(pointsat whichthe segmentsmeet),threesides(the
segmentsthemselves),and threeinteriorangles(formedat eachvertex).All of the followingshapesare
triangles.
You may havelearnedin the past that the sum of the interioranglesin a triangleis always180º.Laterwe
will provethis property, but for now you can use this fact to find missingangles.Otherimportantproperties
of triangleswill be exploredin later chapters.
Example 1
Whichof the figuresbeloware not triangles?To solvethis problem,you mustcarefullyanalyzethe four shapesin the answerchoices.Rememberthat
a trianglehas threesides,threevertices,and threeinteriorangles.ChoiceA fits this description,so it is a
triangle.ChoiceB has one curvedside,so its sidesare not exclusivelyline segments.ChoiceC is also a
triangle.ChoiceD, however, is not a closedshape.Therefore,it is not a triangle.ChoicesB and D are not
triangles.
Example 2
How manytrianglesare in the diagrambelow?