1. 4.4 & 4.5 Proving Triangles Congruent

2. Interactive notebook Entries
Pg & 4-5: Proving Triangles Congruent
Pg. 18 Proving Triangles Congruent (Practice)

3. Objectives:
Use the SSS, SAS, ASA, AAS and HL postulates to test for triangle congruence.

4. Corresponding Parts
In Lesson 4.3, 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

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

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

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

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

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

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

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

12. Hypotenuse-Leg (HL) ABC   ZYX AC  ZX BC  YX RIGHT TRIANGLES A Z B

13. 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 ALWAYS CONGRUENT

14. 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 ALWAYS CONGRUENT

15. The Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
HL correspondence
SSA correspondence
AAA correspondence

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

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

18. 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