6.5 Indirect Proof and Inequalities in One Triangle

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6.5IndirectProofandInequalitiesinOneTriangleIndirectProofsWhatdoesitmeantobeindirect?(akathrowingsubs)Letsdivein!Example1:WritinganIndirectProof.Writeanindirectproofthatinagiventriangle,therecanbeatmostonerightangle.Given:Prove:Solution:

RelatingSidesandAnglesofaTriangleExample2:RelatingsidelengthsandanglemeasureUsingaprotractordrawanytrianglethatisNOTequilateralonscrappaper.Labelsthesidesa,b,&cfromleasttogreatestlengthsrespectively.ThenmeasuretheanglesandlabeltheanlgesA,B,&Cfromleasttogreatestrespectively.

Example3:OrderingAngleMeasuresofaTriangleExample4:OrderingSideLengthsofaTriangleListthesidesoftriangleDEFinorderfromshortesttolongest.

UsingtheTriangleInequalityTheoremUseacompasstocreatethefollowingtriangleswiththegivensegments.

1) 2cm,4cm,5cm

2) 2cm,3cm,5cm

3) 2cm,2cm,5cm

Example5:FindingPossibleSideLengthsAtrianglehasonesideoflength14andanothersideoflength9.Describethepossiblelengthsofthethirdside.Homework7,8,11,12,13,16,17,18,19,21,22,28,29,30,35

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