6.5 indirect proof and inequalities in one triangle

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6.5 Indirect Proof and Inequalities in One Triangle Indirect Proofs What does it mean to be indirect? (aka throwing subs) Lets dive in! Example 1: Writing an Indirect Proof. Write an indirect proof that in a given triangle, there can be at most one right angle. Given: Prove: Solution:

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Page 1: 6.5 Indirect Proof and Inequalities in One Triangle

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

Page 2: 6.5 Indirect Proof and Inequalities in One Triangle

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

Page 3: 6.5 Indirect Proof and Inequalities in One Triangle

Example3:OrderingAngleMeasuresofaTriangleExample4:OrderingSideLengthsofaTriangleListthesidesoftriangleDEFinorderfromshortesttolongest.

Page 4: 6.5 Indirect Proof and Inequalities in One Triangle

UsingtheTriangleInequalityTheoremUseacompasstocreatethefollowingtriangleswiththegivensegments.

1) 2cm,4cm,5cm

2) 2cm,3cm,5cm

3) 2cm,2cm,5cm

Page 5: 6.5 Indirect Proof and Inequalities in One Triangle

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

Page 6: 6.5 Indirect Proof and Inequalities in One Triangle

Page 7: 6.5 Indirect Proof and Inequalities in One Triangle

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