1. Proving Triangles Congruent

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

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

6. Side-Side-Side (SSS)
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

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

8. Side-Angle-Side (SAS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

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

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

11. Angle-Side-Angle (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

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

13. Angle-Angle-Side (AAS)
If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent.

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

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 correspondence
ASA correspondence
SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence

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

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