The easiestway to identifya polygonis to look for a closedfigurewith no curvedsides.If thereis any cur-
vaturein a shape,it cannotbe a polygon.Also,the pointsof a polygonmustall lie withinthe sameplane
(or it wouldn’tbe two-dimensional).
Example 1
Whichof the figuresbelowis a polygon?The easiestway to identifythe polygonis to identifywhichshapesare not polygons.ChoicesB and C each
haveat leastone curvedside.So they cannotbe polygons.ChoiceD has all straightsides,but one of the
verticesis not at the endpointsof the two adjacentsides,so it is not a polygon.ChoiceA is composedentirely
of line segmentsthat intersectat their endpoints.So, it is a polygon.The correctansweris A.
Example 2
Whichof the figuresbelowis not a polygon?All four of the shapesare composedof line segments,so you cannoteliminateany choicesbasedon that
criteriaalone.Noticethat choicesA, B, and D havepointsthat all lie withinthe sameplane.ChoiceC is a
three-dimensionalshape,so it doesnot lie withinone plane.So it is not a polygon.The correctansweris
C.
Convexand ConcavePolygons
Now that you knowhow to identifypolygons,you can beginto practiceclassifyingthem.The first type of
classificationto learnis whethera polygonisconvexorconcave. Thinkof the term concaveas referring
to a cave,or an interiorspace.A concavepolygonhas a sectionthat “pointsinward”towardthe middleof
the shape.In any concavepolygon,thereare at leasttwo verticesthat can be connectedwithoutpassing
throughthe interiorof the shape.The polygonbelowis concaveand demonstratesthis property.