Names:
Math1120
Polygons
Spring2012
YoushouldallrememberVennDiagramsfromlastsemester,butlet’sstartbyreviewingabitbylooking
atthefigurebelow:
Thisisadiagramoftriangles,andsinceeachsetcontainstypesoftriangles,theyareallcontainedwithin
the“triangles”bubble.
Allequilateraltrianglesareacute(allanglesare60degrees!)sotheyarefullycontainedinthe“acute”
bubble.However,isosceles,scaleneandothertrianglesmayalsobeacutesometimes,whichiswhy
thosebubblesoverlapthe“acute”bubble.
Notrianglesarebothisoscelesandscalene,soweshowthisbymakingthe“isosceles”and“scalene”
bubbleshavenooverlap.
1. Addbubblesforrighttrianglesandobtusetrianglestothisfigure(hint:youmaywanttodraw
bubbleswhichareconcaveifyouwanttofitthemintothecorrectplaces)
WHYarewesuddenlydoingVennDiagrams?(Wearesupposedtobedoinggeometry!!)Theansweris
thattheyhelptodemonstratetherelationshipsbetweendifferentobjects.UsingtheVenndiagramon
theothersideofthispage,decideifeachofthefollowingaretrueorfalse.Iffalse,asalways,givea
counterexample.
2. Allequilateraltrianglesareacutetriangles(hint:thisstatementcanbere-wordedas“the
equilateraltrianglebubbleisfullycontainedinsideoftheacutetrianglesbubble.”)
3. Someisoscelestrianglesareequilateral.
4. Somescalenetrianglesareequilateral.
5. Now,we’regoingtoconstructaVenndiagramtohelpreviewdifferenttypesofcurves.
Remember,wehadthefollowingcharacterizationsofcurves:connected,simple,closed,
polygon,convexandconcave.Fillinbubbles,intheappropriateplaces,forthetypesofcurves
notyetincludedinthediagram.
6. Giveanexampleofthefollowing:
a. Asimple,closed,concavecurvewithstraightedges.
b. Acurvewhichisnotsimpleandnotconnected.
c. Aconvexpolygon.
d. Aconnectedcurvewhichisnotclosed.