1. Proving Triangles Congruent
Free powerpoints at

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

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

4. 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. B A C
AB  DE
BC  EF
AC  DF
 A   D
 B   E
 C   F
ABC   DEF E D F

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

6. Side-Side-Side (SSS)
AB  DE
BC  EF
AC  DF
ABC   DEF B A C E D F

7. Side-Angle-Side (SAS)B E F A C D
AB  DE
A   D
AC  DF
ABC   DEF
included
angle

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

9. Included Angle Name the included angle: YE and ES ES and YS YS and YE

10. Angle-Side-Angle (ASA)B E F A C D
A   D
AB  DE
 B   E
ABC   DEF
included
side

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

12. Included Side Name the included side: Y and E E and S S and Y YEES SY

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

14. Hypotenuse-Leg (HL) BA  DF ABC   FDE BC  ED Leg Hypotenuse B F E

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

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

17. The Congruence Postulates
SSS
ASA
SAS
AAS HL
SSA
AAA

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

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

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

21. Name That Postulate
(when possible)

22. Name That Postulate
(when possible)

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

24. Partner Excercise
Indicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
For AAS: