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Notes 4.1-4.3 Triangle Congruence
Learning Targets
I can recognize congruent figures and their
corresponding parts.
I can prove triangles congruent using SSS and
SAS.
I can prove triangles congruent using ASA and
AAS.
Congruence
Two geometric figures with
exactly the same size and
shape.
Corresponding Parts
If all six pairs of corresponding parts
(sides and angles) are congruent, then
the triangles are congruent.
Example 1
1. AB  DE
2. BC  EF
3. AC  DF
4.  A   D
5.  B   E
6.  C   F
ABC   DEF
Do you need all six ?
NO !
SSS
SAS
ASA
AAS
Side-Side-Side or SSS
Side-Side-Side (SSS)
Example 1
1. AB  DE
2. BC  EF
3. AC  DF
ABC   DEF
Included Angle
The angle between two sides
G
I
H
Side-Angle-Side or SAS
Side-Angle-Side (SAS)
1. AB  DE
2. A   D
3. AC  DF
ABC   DEF
included
angle
Included Side
The side between two angles
GI
HI
GH
Included Side
Name the included side:
E
Y
S
Y and E
YE
E and S
ES
S and Y
SY
Angle-Side-Angle or ASA
Angle-Side-Angle (ASA)
1. A   D
2. AB  DE
ABC   DEF
3.  B   E
included
side
Angle-Angle-Side or AAS
Angle-Angle-Side (AAS)
1. A   D
2.  B   E
ABC   DEF
3. BC  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
 SSS
 ASA
 SAS
 AAS
 SSA
 AAA
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
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