5-4 Congruent Triangles. Congruent Triangles An Introduction to Corresponding Parts.
TechMathI - 4.1 - Congruent Triangles
Transcript of TechMathI - 4.1 - Congruent Triangles
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Proving Triangles Congruent
Proving Triangles Congruent
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Two geometric figures with exactly the same size and shape.
The Idea of a CongruenceThe Idea of a Congruence
A C
B
DE
F
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How much do you How much do you need to know. . .need to know. . .
. . . about two triangles to prove that they are congruent?
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Corresponding PartsCorresponding Parts
ABC DEF
B
A C
E
D
F
1. AB DE
2. BC EF
3. AC DF
4. A D
5. B E
6. C F
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Side-Side-Side (SSS)Side-Side-Side (SSS)
1. AB DE
2. BC EF
3. AC DF
ABC DEF
B
A
C
E
D
F
If all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
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Side-Angle-Side (SAS)Side-Angle-Side (SAS)
1. AB DE
2. A D
3. AC DF
ABC DEF
B
A
C
E
D
F
included angle
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The angle between two sides
Included AngleIncluded Angle
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Name the included angle:
YE and ES
ES and YS
YS and YE
Included AngleIncluded Angle
SY
E
E
S
Y
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The Congruence PostulatesThe Congruence Postulates
SSS correspondence
SAS correspondence
ASA correspondence
AAS correspondence
SSA correspondence
AAA correspondence
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Name That PostulateName That Postulate
SASSAS
SSSSSSSSASSA
(when possible)
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Name That PostulateName That Postulate(when possible)
SASASS
AAAAAA
SSASSA
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Name That PostulateName That Postulate(when possible)
SASASS
SASSAS
SASASS
Reflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSSS
AA
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You try! Name That PostulateYou try! Name That Postulate(when possible)
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(when possible)You try! Name That PostulateYou try! Name That Postulate
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Indicate the additional information needed to enable us to apply the specified congruence postulate.
For SAS:
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Point X is the midpoint of AE and BD.
1. Which segments are congruent?
2. Why is <1 congruent to <2?
3. Why is triangle ACB congruent to triangle ECD?