Honors Geometry Section 4.8 cont.Triangle Inequality Proofs

Goals for today’s class:

1. Learn how the TSIT, TAIT, Exterior Angle Inequality Theorem, Parts Theorem and Transitive Property of Inequalities are used in Proofs.

We will use the following theorems about inequalities to do proofs about inequalities in triangles.

Triangle Side Inequality Theorem (TSIT)

In a triangle, if one side of a triangle is longer than another side

of the same triangle, then the angle opposite the longer side is greater than the angle opposite

the smaller side.

Triangle Angle Inequality Theorem (TAIT)

In a triangle, if one angle of a triangle is larger than another

angle of the same triangle, then the side opposite the larger angle is greater than the side opposite

the smaller angle.

Exterior Angle Inequality Theorem (EAIT)

Exterior Angle Inequality Theorem (EAIT)

The measure of an exterior angle of a triangle is greater than either

remote interior angle.

Parts Theorem (PT)The whole is greater than any of its

parts.

A B C

BCAC

ABAC

Transitive Property of Inequalities: (TP of I)

c.a then c,b and ba If

1) 1) Given

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BCAA )2 ITT )2

ABC of

ext.an is BCD )3

angle ext. of Def. )3

AmBCDm )4 (EAIT) Thrm Ineq. Ang. Ext. )4

onSubstituti )5

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1) 1) Given

)

ACBA (TSIT) Thrm Ineq. Side Tri. )

x

ACBC

Prop. Transitive )2

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