1. Lesson 8.04 Triangle Congruence

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

3. If two triangles are congruent, then their corresponding sides and corresponding angles are also congruent or ---- If the corresponding sides and corresponding angles of two triangles are congruent, then the triangles are congruent.

4. Corresponding Parts ABC   DEF AB  DE BC  EF AC  DF  A   D
 B   E
 C   F B A C
ABC   DEF E D F

5. Side-Side-Side (SSS) AB  DE BC  EF AC  DF ABC   DEF
If the three sides of a triangle are congruent to the three sides of another triangle, then the angles MUST be the same (or it wouldn’t form a triangle).

6. Side-Angle-Side (SAS)B E F A C D
AB  DE
A   D
AC  DF
ABC   DEF
If the two sides and the angle IN BETWEEN them are congruent, then the whole triangle must be congruent as well.

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

8. Angle-Side-Angle (ASA)B E F A C D
A   D
AB  DE
 B   E
ABC   DEF
If the two angles and the side IN BETWEEN them are congruent, then the whole triangle must be congruent as well.

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

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

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

12. There is no such thing as an AAA postulate!
Warning: No AAA Postulate
There is no such thing as an AAA postulate!
NOT CONGRUENT E B A C F D

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

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

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

16. 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

17. HW: Name That Postulate
(when possible)

18. HW: Name That Postulate
(when possible)

19. RESOURCES