1. Proving Triangles Congruent
Free powerpoints at

2. Corresponding Parts
In Lesson 4.1, 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

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

4. Do you need to show all sides and all angles?
NO !
SSS
SAS
ASA
AAS HL
You can use 5 methods!

5. Side-Side-Side (SSS) GH  PQ HF  QR GF  PR GHF   PQR H Q R G F P
All three pairs of corresponding sides are congruent.
GH  PQ
HF  QR
GF  PR
GHF   PQR H G F Q P R

6. Side-Angle-Side (SAS)
Uses two sides and the included angle. B F E C A D
BC  FD
C   D
AC  ED
ABC   EFD
included
angle

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

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

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

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

11. Angle-Side-Angle (ASA)
Uses two angles and the included side. B P N G H K
G   K
GB  KP
 B   P
GBH   KPN
included
side

12. Angle-Angle-Side (AAS)
Uses two angles and a non-included side. C X T D M G
D   G
 C   X
CM  XT
DMC   GTX
Non-included
side

13. Hypotenuse-Leg (HL) AC  ZY (leg) ABC   ZXY 2. AB  ZX (hypotenuse)
Needs a right triangle
Uses the hypotenuse and one other side (leg).
AC  ZY (leg)
ABC   ZXY
2. AB  ZX (hypotenuse)
To use hypotenuse-leg, you MUST have a right triangle!!
The hypotenuse is ALWAYS opposite the right angle.

14. Methods that DO NOT WORK!
The following methods cannot be used to prove triangles congruent.

15. There is no such thing as an ASS (or SSA) postulate!
Warning: No A-S-S
(“Donkey Theorem”)
There is no such thing as an ASS (or 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. Not enough information
Sometimes you won’t have enough information given to determine if 2 triangles are congruent.

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

19. Name That Postulate
(when possible)
SAS
ASA
ASS
Not
SSS

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

21. Name That Postulate SAS SAS ASS SAS Vertical Angles Reflexive Property
(when possible)
Vertical Angles
Reflexive Property
SAS
SAS
ASS
Reflexive Property
Vertical Angles
SAS

22. HW: Name That Postulate
(when possible)
SSS
Not enough information
No donkey theorem!
ASS not allowed
AAA not allowed

23. HW: Name That Postulate
(when possible)

24. 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:

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