1. Proving Triangles Congruent
Obj: SWBAT: 1) State the requirements for Congruency 2) Use the ASA and AAS Postulates to prove Triangle Congruency 3) Define, identify, and use the concept of an Included Side
M11.C Identify and/or use properties of congruent and similar polygons or solids.

2. Angle-Side-Angle (ASA)B E F A C D
A   D
AB  DE
 B   E
ABC   DEF
Included side
ASA: If 2 <s of 1 triangle are  to 2 <s of another triangle and the included side of 1 triangle is  to the included side of another triangle, then the 2 triangles are .

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

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

5. Example
From the information in the diagram, can you prove that ΔFDG and ΔFDE are congruent? Explain.
yes; AAA
yes; ASA
yes; SSS no

6. Angle-Angle-Side (AAS)B E F A C D
A   D
 B   E
BC  EF
ABC   DEF
Non-included
side
AAS: If 2 <s of 1 triangle are  to 2 <s of another triangle and the non-included side of 1 triangle is  to the non-included side of another triangle, then the 2 triangles are .

7. There is no such thing as an ASS postulate!
Warning: No ASS Postulate
There is no such thing as an ASS postulate!
NOT CONGRUENT

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

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

10. Name That Postulate
(when possible)
SAS
ASA
ASS
SSS

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

12. Determine which triangles are congruent by AAS using the information in the diagram below.
ΔABE ≅ ΔCBE
ΔABF ≅ ΔEDF
ΔABE ≅ ΔEDA
ΔADC ≅ ΔEBC
Name the postulate that proves that the triangles are congruent. (Hint: What type of triangle is this and what are its special properties?)
SAS
AAS
ASA
ASS

13. 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: