1. 5-5 & 5-6 SSS, SAS, ASA, & AAS

2. Proving Triangles 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
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

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. 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
(when possible)
AAA
ASA
SSA
SAS

20. 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

21. HW: Name That Postulate
(when possible)

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

25. Write a congruence statement for each pair of triangles represented.B D A C E F

26. Slide 1 of 2
1-1a

27. Slide 1 of 2
1-1b

28. 5.6
ASA and AAS

29. Before we start…let’s get a few things straightC X Z Y
INCLUDED SIDE

30. Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side

31. Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT included

32. Your Only Ways To Prove Triangles Are Congruent
SSS
SAS
ASA
AAS
Your Only Ways To Prove Triangles Are Congruent

33. 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

34. Ex 1
DEF
NLM

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. Slide 2 of 2
1-2a

43. Slide 2 of 2
1-2b

44. Slide 2 of 2
1-2b

45. Slide 2 of 2
1-2c

46. (over Lesson 5-5)
Slide 1 of 2
1-1a

47. (over Lesson 5-5)
Slide 1 of 2
1-1b

48. Slide 1 of 2
1-1a

49. Slide 1 of 2
1-1b

50. Slide 1 of 2
1-1b

51. Slide 1 of 2
1-1c

52. Slide 2 of 2
1-2a

53. Slide 2 of 2
1-2a

54. Slide 2 of 2
1-2a

55. Slide 2 of 2
1-2a