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# Geometry Congruence

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```Proving Triangles
Congruent
The Idea of a Congruence
Two geometric figures with
exactly the same size and
shape.
F
B
A
C
E
D
How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?
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 пЃЂ DE
2. BC пЃЂ EF
3. AC пЃЂ DF
4. пѓђ A пЃЂ пѓђ D
5. пѓђ B пЃЂ пѓђ E
6. пѓђ C пЃЂ пѓђ F
пЃ„ABC пЃЂ пЃ„ DEF
Do you need all six ?
NO !
SSS
SAS
ASA
AAS
Side-Side-Side (SSS)
1. AB пЃЂ DE
2. BC пЃЂ EF
3. AC пЃЂ DF
пЃ„ABC пЃЂ пЃ„ DEF
Side-Angle-Side (SAS)
1. AB пЃЂ DE
2. пѓђA пЃЂ пѓђ D
3. AC пЃЂ DF
пЃ„ABC пЃЂ пЃ„ DEF
included
angle
Included Angle
The angle between two sides
пѓђG
пѓђI
пѓђH
Included Angle
Name the included angle:
E
Y
S
YE and ES
пѓђE
ES and YS
пѓђS
YS and YE
пѓђY
Angle-Side-Angle (ASA)
1. пѓђA пЃЂ пѓђ D
2. AB пЃЂ DE
пЃ„ABC пЃЂ пЃ„ DEF
3. пѓђ B пЃЂ пѓђ E
include
d
side
Included Side
The side between two angles
GI
HI
GH
Included Side
Name the included angle:
E
Y
S
пѓђY and пѓђE
YE
пѓђE and пѓђS
ES
пѓђS and пѓђY
SY
Angle-Angle-Side (AAS)
1. пѓђA пЃЂ пѓђ D
2. пѓђ B пЃЂ пѓђ E
пЃ„ABC пЃЂ пЃ„ DEF
3. BC пЃЂ EF
Non-included
side
Warning: No SSA Postulate
There is no such
thing as an SSA
postulate!
E
B
F
A
C
D
NOT CONGRUENT
Warning: No AAA Postulate
There is no such
thing as an AAA
postulate!
E
B
A
C
D
NOT CONGRUENT
F
The Congruence Postulates
пЃ† SSS
correspondence
пЃ† ASA
correspondence
пЃ† SAS
correspondence
пЃ† AAS
correspondence
пЃ† SSA
correspondence
пЃ† AAA
correspondence
Name That Postulate
(when possible)
SAS
SSA
ASA
SSS
Name That Postulate
(when possible)
AAA
SAS
ASA
SSA
Name That Postulate
(when possible)
Reflexive
Property
SAS
Vertical
Angles
SAS
Vertical
Angles
SAS
Reflexive
Property
SSA
HW: Name That Postulate
(when possible)
HW: Name That Postulate
(when possible)
LetвЂ™s Practice
to enable us to apply the specified
congruence postulate.
For ASA:
пѓђB пЃЂ пѓђD
For SAS:
AC пЃЂ FE
For AAS:
пѓђA пЃЂ пѓђF
HW
to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:
For AAS:
This powerpoint was kindly donated to
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visit and I hope it will help in your teaching.
```
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