1. Proving Triangles Congruent

2. Some basic things we need to know!
We represent angles using the symbol _____.
We represent sides using a line above the letters that represent it ___.
The symbol  means _______.
< AB
Congruent

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

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

5. Corresponding Parts
There are 6 corresponding parts in a triangle. 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

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

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

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

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

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

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

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

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

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

15. Hypotenuse-Leg (HL) ABC   DEF In a Right Triangle hyp  hyp
Leg  Leg

16. 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

17. 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

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

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

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

21. 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

22. CW: Name That Postulate
(when possible)

23. CW: Name That Postulate
(when possible)

24. STOP HERE

25. 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:

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

27. Angle-Angle (AA)
A   D
 C   C
(Vertical Angles) ABC   DEF