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Geometry Unit4:CongruenceProofs
Ms.Talhami 1
GeometryUnit4:CongruenceProofs
Name_________________
Geometry Unit4:CongruenceProofs
Ms.Talhami 2
HelpfulVocabulary
Word Definition/Explanation Examples/HelpfulTips
Geometry Unit4:CongruenceProofs
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Whatdoesitmeanfortwotrianglestobecongruent?
Whatdoesitmeanfortwotrianglestobecongruent?
CongruenceStatement/CorrespondingParts1. Youmustnametheverticesofthetriangleinorder! Thepartsofthetrianglesarecorresponding.
a b c d
e f
ProvingTrianglesCongruent
5methods:1. 3. 5.2. 4.
Geometry Unit4:CongruenceProofs
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Examplesofthe5MethodsUsedtoProveTrianglesCongruent
HiddenCongruentParts-VerticalAngles
Theorem:IntersectingLinesformCongruentVerticalAngles
HiddenCongruentParts-ReflexivePropertyProperty:Reflexive(SharedSides/SharedAnglesarecongruent).
Geometry Unit4:CongruenceProofs
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ExtraPracticeBasedonthemarkings,determinewhatmethodisneededtoprovethetrianglescongruent.(SSS,SAS,ASA,AAS,HL)1.
2.
3.
4.
5.
6.
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9.
10.
Geometry Unit4:CongruenceProofs
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UsingGivenInformationtoMarkCongruentParts.Determinewhythetrianglesarecongruent.1.Given: Given: Given: Prove:rABC≅rXYZ
2.Given: Given: Given: Prove:rKJM≅r
3.Given: Given: Given: Prove:rWAY≅r
4.Given: Given: Given: Prove:rABC≅r
Geometry Unit4:CongruenceProofs
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5.Given: Given: Prove:rACE≅r
6.Given: Given: Prove:rARS≅r
ExtraPractice
7. Usingthecongruencestatement .Completeeachofthefollowing:
a d
b e
c f 8. Whichstatementscanyouusetoprove bytheASApostulate?
I. II. III. IV.
(a)I,II,andIV (b)I,III,andIV (c)II,III,andIV (d)I,II,andIII (e)noneoftheabove Determinewhatmethodcanbeusedtoprovethetrianglescongruent.Completeeachcongruencestatement.
9.Given: Given: Given: Prove:rKJM≅r
10.Given: Given: Given:Prove:rABC≅r
CT ≅ G ≅
AC ≅ ≅
A ≅ ≅
Geometry Unit4:CongruenceProofs
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11.Given: Given: Given:
Prove:rADB≅r
12.Given: Given: Given:
Prove:rABC≅r
Geometry Unit4:CongruenceProofs
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Geometry Unit4:CongruenceProofs
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Geometry Unit4:CongruenceProofs
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Geometry Unit4:CongruenceProofs
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Are the following pairs of triangles congruent? If YES, create a congruence statement and name the congruence method.
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Geometry Unit4:CongruenceProofs
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Geometry Unit4:CongruenceProofs
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ExtraPractice
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DoNow:
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1.
2.
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Geometry Unit4:CongruenceProofs
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Geometry Unit4:CongruenceProofs
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Geometry Unit4:CongruenceProofs
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Geometry Unit4:CongruenceProofs
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PartsofTrianglesinProofsAltitudes
Medians
DifferentTypesofTrianglesinProofs
RightTriangles
Equilateral/EquiangularTriangles
IsoscelesTriangles
Geometry Unit4:CongruenceProofs
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Practice1
2
3
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Geometry Unit4:CongruenceProofs
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Geometry Unit4:CongruenceProofs
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ApplyingAdditionandSubtractiontoTriangleProofs
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Geometry Unit4:CongruenceProofs
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DoNow1
2
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TransitivePropertyandSubstitutionPostulate
TransitiveProperty
SubstitutionPostulate
Practice
DoNow
a)Howmanydifferenttrianglescanyoufindinthefollowingimage?
b)Namethreedifferentpairsofcongruenttriangles.
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6.
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MixedPractice1
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2
3
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4
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