1. Bell Work Wednesday, August 7, 2013
List two acts that will results in a student having a teacher conference.

2. Standard
Congruency postulates, SSS, SAS, ASA, & AAS

3. Essential Question
How does learning the congruency postulates help me prove that two triangle are congruent?

4. Closing
See nature by numbers video:
Homework Assignment #1 – You saw the video, Nature by Numbers. Submit a picture of something from nature and point out one or several geometric shapes similarly to what you saw in the video. Due: Thursday in class.

5. The congruence postulates: SSS, SAS, ASA, & AAS

6. Proving Triangles Congruent

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

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

9. 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

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

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

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

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

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

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

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

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

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

19. 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

20. 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

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

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

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

24. 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

25. HW: Name That Postulate
(when possible)

26. HW: Name That Postulate
(when possible)

27. 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:

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

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

30. Slide 1 of 2
1-1A

31. Slide 1 of 2
1-1B

32. 5.6
ASA and AAS

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

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

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

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

37. 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

38. Ex 1
DEF
NLM

39. 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

40. 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

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 4 G I H J K
ΔGIH  ΔJIK by AAS

42. 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

43. 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

44. 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

45. 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

46. Slide 2 of 2
1-2A

47. Slide 2 of 2
1-2B

48. Slide 2 of 2
1-2B

49. Slide 2 of 2
1-2C

50. (over Lesson 5-5)
Slide 1 of 2
1-1A

51. (over Lesson 5-5)
Slide 1 of 2
1-1B

52. Slide 1 of 2
1-1A

53. Slide 1 of 2
1-1B

54. Slide 1 of 2
1-1B

55. Slide 1 of 2
1-1C

56. Slide 2 of 2
1-2A

57. Slide 2 of 2
1-2A

58. Slide 2 of 2
1-2A

59. Slide 2 of 2
1-2A