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
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

6. Side-Side-Side (SSS) AB  DE BC  EF AC  DF ABC   DEF
If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent

7. Side-Angle-Side (SAS)B E F A C D
AB  DE
A   D
AC  DF
ABC   DEF
included
side
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent

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
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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

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

13. Angle-Angle-Side (AAS)B E F A C D
A   D
 B   E
BC  EF
ABC   DEF
Non-included
side
If 2 angles and a non-included side of 1 triangle are congruent to 2 angles and the corresponding non-included side of another triangle, then the 2 triangles are congruent

14. 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

15. 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

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

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

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

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

20. HW: Name That Postulate
(when possible)

21. HW: Name That Postulate
(when possible)

22. 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:

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