triangle congruence

1. Proving Triangles
Congruent

2. The Idea of a Congruence
Two geometric figures with
exactly the same size and
shape.
F

3. A C E D
)
How much do you need
to know. . .

4. . . . about two triangles
to prove that
they
e congruent?
Corresponding Parts
In Lesson 4.2, you learned that if all
six pairs of corresponding parts (sides

5. and angles) are congruent, then the
triangles are congruent.
• AB =
DE
• BC =
EF
• AC =
DF
V z A
= z
B
DAABC = A
DEF

6. V Z C ‘ = Z F

7. Do you need all six ?
NO!

8. Side-Side-Side (SSS)

9. B C * EF
AC a DF
AABC ^ A DEF
)

10. Side-Angle-Side (SAS)

11. • AB
•
z A
• AC
1
DE
= Z ^
* DF °
AABC ^ A DEF
include
d angle
Included Angle

12. The angle between two sides
z G
)
z I z H

13. Y S
Included Angle
Name the included angle:
YE and ES z E
ES and YS z S
YS and YE z Y

14. Angle-Side-Angle (ASA)

15. •
z A
• AB
• . B
= Z.
D
DEo
O
/v/
= Z.
E
T
&ABC ^ A DEF

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

17. Y
)
Included Side
S

18. Angle-Angle-Side (AAS)

20. Warning: No SSA Postulate
B
A
1
There is no such
thing as an SSA
postulate!
E
F
NOT CONGRUENT

21. Warning: No AAA Postulate
B
A
There is no such
thing as an AAA
postulate!
E
C F
) D

22. NOT CONGRUENT
The Congruence Postulates
^SSS correspondence ^ASA
correspondence ^SAS correspondence
^AAS correspondence

23. ) ^AAA correspondence

24. Name That Postulate
(when possible)

25. Name That Postulate
SAS ASA
SSS
(when possible)

26. Name That Postulate

27. Name That Postulate
SAS
(when possible)

28. Name That Postulate
Vertical
Reflexive Property SAS SAS

29. Name That Postulate
Vertical
Angles
SAS Reflexive
Property

30. Name That Postulate
(when possible)

31. Name That Postulate
(when possible)

32. Let’s Practice
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:

33. For AAS: ZA = ZF
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.

34. For ASA:
For SAS:
For AAS:

36. Determine if whether each pair of triangles is cong
SSS, SAS, ASA, or AAS. If it is not possible to pro
that they are congruent, write not possible.
by
Ex 4 GK
H J

37. AGIH s AJIK by A
Determine if whether each pair of triangles is congruent
b SSS, SAS, ASA, or AAS. If it is not possible to prove
that they are congruent, write not possible.

39. AABC a AEDC by
ASA
Determine if whether each pair of triangles is congruent
b SSS, SAS, ASA, or AAS. If it is not possible to prove
that they are congruent, write not possible.
Ex 6 AE

40. B D

41. AACB AECD by S

42. Determine if whether each pair of triangles is congruewby
SSS, SAS, ASA, or AAS. If it is not possible to provp
that they are congruent, write not possible.
Ex 7
M L
K

43. AJMK = ALKM by SAS or ASA
)
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
JT

44. V U

45. Not possible