1. Proving Triangles Congruent

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

3. Corresponding Parts ABC   DEF
You will learn that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.
AB  DE
BC  EF
AC  DF
 A   D
 B   E
 C   F B A C
ABC   DEF E D F

4. triangles are congruent?
How many of the 6 relationships
do you need. . .
. . .to prove that 2
triangles are congruent?

5. Do you need ALL six ?
NO!
SSS
SAS
ASA
AAS
BUT ORDER MATTERS!!!!

6. Side-Side-Side (SSS) S AB  DE S BC  EF S AC  DF ABC   DEF B E F

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

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

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

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

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

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

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

14. Recap SSS correspondence ASA correspondence SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence
BUT ORDER MATTERS!!!!

15. No ASS Postulate because the triangles may or may not be congruent.
Warning! No SSA Postulate
No ASS Postulate because the triangles may or may not be congruent.
NOT CONGRUENT

16. Warning! No AAA Postulate
No AAA Postulate because congruent angles do not
always imply congruent sides!
NOT CONGRUENT 3 8 3 8 3 8

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

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

19. 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

20. HW: Name That Postulate
(when possible) AS
SSS
Reflexive Property
ASS
AAA

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

22. 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:

23. OYO = On Your Own N  V MK  UT M  U
Indicate the additional information needed to enable us to apply the specified congruence postulate.
N  V
For ASA:
For SAS:
MK  UT
For AAS:
M  U

24. ONLY works for right triangles!
Hypotenuse-Leg (HL)
QRS and  XYZ are right triangles
H QS  XZ
L RS  YZ
QRS   XYZ
ONLY works for right triangles!

25. AAS SAS HL ASS Name that Postulate Vertical Angles Reflexive Property
(when possible)
Vertical Angles
AAS
SAS
Reflexive Property
Reflexive Property HL
ASS

26. Another Big Idea: CPCTC
Stands for “Corresponding Parts of Congruent Triangles are Congruent”
Once you have already proved triangles congruent, you know that all corresponding sides and angles are congruent.
Recall: If then
AB  DE
BC  EF
AC  DF
 A   D
 B   E
 C   F
ABC   DEF B A C E D F

30. This powerpoint was kindly donated to www.worldofteaching.com
is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.