1. Today you will need your textbook only.

2. Modules 5 and 6 SSS, SAS, ASA, & AAS

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

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

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

12. 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

13. 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

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

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

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

17. 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

18. HW: Name That Postulate
(when possible)

19. HW: Name That Postulate
(when possible)

20. 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:

21. Alt Int Angles are congruent given parallel lines
Things you can mark on a triangle when they aren’t marked.
Overlapping sides are congruent in each triangle by the REFLEXIVE property
Alt Int Angles are congruent given parallel lines
Vertical Angles are congruent

22. Ex 2
What other pair of angles needs to be marked so that the two triangles are congruent by AAS? F D E M L N

23. Ex 3
What other pair of angles needs to be marked so that the two triangles are congruent by ASA? F D E M L N

24. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
Ex 4 G I H J K
ΔGIH  ΔJIK by AAS

25. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. B A C E D
Ex 5
ΔABC  ΔEDC by ASA

26. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
Ex 6 E A C B D
ΔACB  ΔECD by SAS

27. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
Ex 7 J K L M
ΔJMK  ΔLKM by SAS or ASA

28. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
Ex 8 J T L K V U
Not possible

29. Homework Problems (due Thursday)
Pages , #’s 3-6
Page 240, # 14
Page 250, #’s 2-7
For tomorrow, be prepared with your proof notebook as we will begin practicing triangle congruence proofs.