The document discusses the conditions necessary to prove the congruence of triangles, outlining that six pairs of corresponding parts (sides and angles) between two triangles must be congruent. It details various congruence postulates: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS), while explicitly noting that the Side-Side-Angle (SSA) and Angle-Angle-Angle (AAA) conditions do not establish congruence. Additionally, it provides practice examples and resources for further learning on the topic.

1. Proving Triangles
Congruent

2. Two geometric figures with
exactly the same size and
shape.
The Idea of a Congruence
A C
B
D
E
F

3. How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?

4. In Lesson 4.2, you learned that if all
six pairs of corresponding parts (sides
and angles) are congruent, then the
triangles are congruent.
Corresponding Parts
ABC   DEF
1. AB  DE
2. BC  EF
3. AC  DF
4.  A   D
5.  B   E
6.  C   F

5. Do you need all six ?
NO !
SSS
SAS
ASA
AAS

6. Side-Side-Side (SSS)
1. AB  DE
2. BC  EF
3. AC  DF
ABC   DEF

7. Side-Angle-Side (SAS)
1. AB  DE
2. A  D
3. AC  DF
ABC   DEF
included
angle

8. The angle between two sides
Included Angle
 G  I  H

9. Name the included angle:
YE and ES
ES and YS
YS and YE
Included Angle
S
Y
E
 E
 S
 Y

10. Angle-Side-Angle (ASA)
1. A   D
2. AB  DE
3.  B   E
ABC   DEF
include
d
side

11. The side between two angles
Included Side
GI HI GH

12. Name the included angle:
Y and E
E and S
S and Y
Included Side
S
Y
E
YE
ES
SY

13. Angle-Angle-Side (AAS)
1. A  D
2. B  E
3. BC  EF
ABC   DEF
Non-included
side

14. Warning: No SSA Postulate
A C
B
D
E
F
NOT CONGRUENT
There is no such
thing as an SSA
postulate!

15. Warning: No AAA Postulate
A C
B
D
E
F
There is no such
thing as an AAA
postulate!
NOT CONGRUENT

16. The Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence

17. Name That Postulate
SAS
ASA
SSS
SSA
(when possible)

18. Name That Postulate
(when possible)
ASA
SAS
AAA
SSA

19. Name That Postulate
(when possible)
SAS
SAS
SAS
Reflexive
Property
Vertical
Angles
Vertical
Angles
Reflexive
Property SSA

20. HW: Name That Postulate
(when possible)

21. (when possible)
HW: Name That Postulate

22. Let’s Practice
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:
B  D
For AAS: A  F
AC  FE

23. 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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