Proving Triangles Congruent

1
Proving Triangles Congruent
jc-schools.net/PPT/geometrycongruence.ppt
2
Angle-Side-Angle (ASA)

• Postulate 8-3
• If two angles and the included side of one
  triangle are congruent to two angles and the
  included side of another triangle, then the two
  triangles are congruent.

3
Angle-Side-Angle (ASA)


B

E






F
A



C
D

1. ?A ? ? D
2. AB ? DE
3. ? B ? ? E

?ABC ? ? DEF
included side
jc-schools.net/PPT/geometrycongruence.ppt
4
Angle-Angle-Side (AAS)

• Theorem 8-1
• If two angles and the nonincluded side of one
  triangle are congruent to two angles and the
  nonincluded side of another triangle, then the
  two triangles are congruent.

5
Angle-Angle-Side (AAS)


B

E






F
A



C
D

1. ?A ? ? D
2. ? B ? ? E
3. BC ? EF

?ABC ? ? DEF
Non-included side
jc-schools.net/PPT/geometrycongruence.ppt
6
Warning No SSA Postulate
There is no such thing as an SSA postulate!
E
B
F
A
C
D
NOT CONGRUENT
jc-schools.net/PPT/geometrycongruence.ppt
7
Warning No AAA Postulate
There is no such thing as an AAA postulate!
E
B
A
C
F
D
NOT CONGRUENT
jc-schools.net/PPT/geometrycongruence.ppt
8
The Congruence Postulates
jc-schools.net/PPT/geometrycongruence.ppt
9
Name That Postulate
(when possible)
SAS
ASA
SSA
SSS
jc-schools.net/PPT/geometrycongruence.ppt
10
Name That Postulate
(when possible)
AAA
ASA
SSA
SAS
jc-schools.net/PPT/geometrycongruence.ppt
11
Lets Practice
Indicate the additional information needed to
enable us to apply the specified congruence
postulate.
For ASA
?B ? ?D
For SAS
?A ? ?F
For AAS
jc-schools.net/PPT/geometrycongruence.ppt
12
Another
Indicate the additional information needed to
enable us to apply the specified congruence
postulate.
For ASA
For SAS
For AAS
jc-schools.net/PPT/geometrycongruence.ppt