BigIdeasCh5Notes

Geometry Name___________________________________________ Date____________________________Period__________

Chapter5CongruentTriangles

Ch5.1AnglesofTriangles

Classifica8onbyAngleMeasure

Classifica8onbySideMeasure

ClassifytheTriangle

AnglesoftheTriangle

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BigIdeasCh5Notes

Whatis� ?Andwhy?

Solve

Whatisthemeasureofangle6?

Prac8ce:

m∠1+m∠2+m∠3

Triangle Sum Theorem

Exterior Angle Theorem

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Ch5.2CongruentPolygons

Vocabulary

CongruentFigures:__________________________________________________________________________________________

RigidMo8onProof:Provingtwopolygonsarecongruent.

Proper8esofcongruentpolygons

Twopolygonsarecongruentwhen:

1._____________________________________________________________________________________

2._____________________________________________________________________________________

Forthediagramontheright:

�

Forthefiguresbelow,supposeyouaregiventhat� .WhatdoyouautomaNcallyknow?

ABCD≅

ΔABC ≅ ΔDEF

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Given:Thetwotrianglesarecongruent

a.� ______________

b.� _______________

c.� ______________because____________________________________________

Then� _____________because________________________________________

d.� ______________because________________________________________

Then________________||_____________because________________________________________

Proper8esofTriangleCongruence

ΔPAL ≅

PA ≅

∠1≅

PA ||

∠2 ≅

Reflexive

Symmetric

Transitive

Third Angles Theorem

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Given� bisects� ,� bisects� Prove:thetwotrianglesarecongruent

Statements Reasons

Ch5.3ProvingTriangleCongruencebySAS

Statements Reasons

Whicharecongruent,andwhyorwhynot?

AD BE BE AD

Side-Angle-Side (SAS) Congruence Theorem

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Ch5.4EquilateralandIsoscelesTriangles

IsoscelesTriangle

Listthetriangleparts.

Completethestatementsusingthefiguretotheright.

1.If� ,then∠______________≅∠______________

2.If� ,then______________≅______________

Base Angles Theorem

Converse of theBase Angles Theorem

HG ≅ HK

∠KHJ ≅ ∠KJH

Corollary toBase Angles Theorem

Corollary to the Converse of the

Base Angles Theorem

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Solveforx.

Ch5.5ProvingTriangleCongruencebySSS

Prove:

Statements Reasons

Side-Side-Side (SSS) Congruence Theorem

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Determineif∆ABCand∆DEFarecongruentusingSSS.Ifso,writetheircongruencestatement.

1)A(−2,−2),B(4,6),C(4,−2),D(5,7),E(5,1),F(13,1)

2)A(9,0),B(0,0),C(6,5),D(0,−1),E(6,−6),F(9,−1)

Prove:

Statements Reasons

Hypotenuse-Leg (HL) Congruence Theorem

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Ch5.6ProvingTriangleCongruencebyASAandAAS

Whicharecongruentandwhy?

Prove:

Statements Reasons

Angle-Side-Angle (ASA) Congruence

Theorem

Angle-Angle-Side (AAS) Congruence

Theorem

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BigIdeasCh5Notes

Prove:

Statements Reasons

SummaryofTriangleCongruenceTheorems

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Ch5.7UsingCongruentTriangles

Inthischapter,ifweprove_________________________________________________arecongruent,

thenthe____________________________________________________________mustbecongruent!

ThisreasoniscalledCPCTCwhichstandsfor

____________________________________________________________________________________________________________

Writeaplantoprove� .

Prove:

Statements Reasons

Ch5.8CoordinateProof(skip)

ΔPTU ≅ ΔUQP

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