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Ch 5. Proving Triangles
Congruent
(Sec 5.4 – Sec 5.6)
Objectives: What we’ll
learn…
• Identify corresponding parts of
congruent triangles.
• Use SSS and SAS tests for
congruence.
• Use ASA and AAS tests for
congruence.
The Idea of a Congruence
Two geometric figures with
exactly the same shape and
size.
NOT Congruent!!!
F
B
A
C
E
D
Yes, they are Congruent.
Why Congruence?
When factory manufactures cars, each car must be identical
(congruent)……
If not congruent = defects= Company losing $$$$$$
Why triangles?
• It’s a simple polygon!!!
How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?
Corresponding Parts
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
5.  B   E
6.  C   F
ABC  DEF
Do you need all six ?
NO !
SSS
SAS
ASA
AAS
Side-Side-Side (SSS)
1. AB  DE
2. BC  EF
3. AC  DF
ABC   DEF
Side-Angle-Side (SAS)
1. AB  DE
2. A   D
3. AC  DF
ABC  DEF
included
angle
Included Angle
The angle between two sides
G
I
H
Included Angle
Name the included angle:
E
Y
S
YE and ES
E
ES and YS
S
YS and YE
Y
Angle-Side-Angle (ASA)
1. A   D
2. AB  DE
ABC   DEF
3.  B   E
included
side
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-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!
TRIANGLES NOT CONGRUENT
Warning: No AAA Postulate
There is no such
thing as an AAA
postulate!
E
B
A
C
D
F
All congruent angles, but NOT congruent in size.
The Congruence Postulates
 SSS
correspondence
 ASA
correspondence
 SAS
correspondence
 AAS
correspondence
 SSA correspondence
 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)
Included Angle
Included Side
Hexagon vs. Pentagon
Hint: No AAA Postulate
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
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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