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Proving Triangles
Congruent
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The Idea of a Congruence
Two geometric figures with
exactly the same size and
shape.
F
B
A
C
E
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D
How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?
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Corresponding Parts
In Lesson 4.2, you learned that if all
six pairs of corresponding parts (sides
and angles) are congruent, then the
triangles are congruent.
1. AB  DE
2. BC  EF
3. AC  DF
4.  A   D
ABC   DEF
5.  B   E
6.  C   F
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Do you need all six ?
NO !
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SSS
SAS
ASA
AAS
Side-Side-Side (SSS)
1. AB  DE
2. BC  EF
ABC   DEF
3. AC  DF
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Side-Angle-Side (SAS)
1. AB  DE
2. A   D
3. AC  DF
ABC   DEF
included
angle
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Included Angle
The angle between two sides
G
I
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H
Included Angle
Name the included angle:
E
Y
S
YE and ES
E
ES and YS
S
YS and YE
Y
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Angle-Side-Angle (ASA)
1. A   D
2. AB  DE
ABC   DEF
3.  B   E
include
d
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side
Included Side
The side between two angles
GI
HI
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GH
Included Side
Name the included angle:
E
Y
S
Y and E
YE
E and S
ES
S and Y
SY
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Angle-Angle-Side (AAS)
1. A   D
2.  B   E
ABC   DEF
3. BC  EF
Non-included
side
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Warning: No SSA Postulate
There is no such
thing as an SSA
postulate!
E
B
F
A
C
D
NOT
CONGRUENT
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Warning: No AAA Postulate
There is no such
thing as an AAA
postulate!
E
B
A
C
D
NOT
CONGRUENT
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F
The Congruence Postulates
 SSS
correspondence
 ASA
correspondence
 SAS
correspondence
 AAS
correspondence
 SSA correspondence
 AAA
correspondence
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Name That Postulate
(when possible)
SAS
ASA
SSA
SSS
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Name That Postulate
(when possible)
AAA
ASA
SSA
SAS
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Name That Postulate
(when possible)
Reflexive
Property
SAS
Vertical
Angles
Vertical
Angles
SAS
Reflexive
SAS
Property
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SSA
HW: Name That Postulate
(when possible)
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HW: Name That Postulate
(when possible)
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Let’s Practice
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
B  D
For SAS:
AC  FE
For AAS:
A  F
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HW
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:
For AAS:
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