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Geom 5.5­5.6 ­ Proving Triangles Congruent ­ SSS, SAS, ASA, AAS
Proving Triangles Congruent: SASASA Method
Two triangles are congruent iff all of their corresponding parts (angles and sides) are congruent.
If ΔABC ≅ ΔDEF, then:
D
A
C
B
E
F
Proving Triangles Congruent: SSS Method
If all of the sides of ΔABC ≅ all of the sides of ΔDEF, then by Side­Side­Side Postulate, ΔABC ≅ ΔDEF:
D
A
C
B
F
E
Geom 5.5­5.6 ­ Proving Triangles Congruent ­ SSS, SAS, ASA, AAS
Proving Triangles Congruent: SAS Method
If two of the sides of ΔABC and the angle between them ≅ two of the sides of ΔDEF and the angle between them, then by Side­Angle­Side Postulate, ΔABC ≅ ΔDEF:
D
A
C
F
B
E
Proving Triangles Congruent: ASA Method
If two of the angles of ΔABC and the side between them ≅ two of the angles of ΔDEF and the side between them, then by Angle­Side­Angle Postulate, ΔABC ≅ ΔDEF:
D
A
C
B
F
E
Geom 5.5­5.6 ­ Proving Triangles Congruent ­ SSS, SAS, ASA, AAS
Proving Triangles Congruent: AAS Method
If two of the angles of ΔABC and a side not between them ≅ two of the angles of ΔDEF and the corresponding side not between them, then by the Angle­Angle­Side Theorem, ΔABC ≅ ΔDEF:
D
A
E
F
B
C
Proving Triangles Congruent: AAA Method?
If all of the angles of ΔABC ≅ all of the angles of ΔDEF, then is ΔABC ≅ ΔDEF?
D
A
F
C
B
E
Geom 5.5­5.6 ­ Proving Triangles Congruent ­ SSS, SAS, ASA, AAS
Proving Triangles Congruent: SSA Method?
If two of the sides of ΔABC and an angle not between them ≅ two of the sides of ΔDEF and the corresponding angle not between them, then by the Angle­Side­Side Theorem, is ΔABC ≅ ΔDEF ?
D
A
C
B
F
F
E
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