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Triangle Congruence Postulates
Contributed by: Miles
Match each congruence postulate with its abbreviation.
Congruence Postulate
Angle - Side - Angle
Side - Angle - Side
Angle - Angle - Side
Hypotenuse - Leg
Side - Side - Side
Triangle Congruence Postulates
Abbreviation
AAS
?
ASA
?
SSS
?
SAS
?
HL
?
Use the diagram to name the included angle between the given pair of the sides.
AB and BC
BC and CD
AB and BD
Sides
Included Angle
∠BCD
?
∠CBA
?
​∠DBA
?
Decide whether enough information is given to prove 
that the triangles are congruent. 
Yes, congruent by AAS
​Yes, congruent by HL
Yes, congruent by SSS
Yes, congruent by SAS
Not necessarily congruent
​Yes, congruent by ASA
Decide whether enough information is given to prove 
that the triangles are congruent. 
Yes, congruent by SSS
Yes, congruent by SAS
Yes, congruent by AAS
​Yes, congruent by HL
​Yes, congruent by ASA
Not necessarily congruent
Decide whether enough information is given to prove
the triangles are congruent:
Yes, by SSS only
Yes, by ASA only
Yes, by AAS only
Yes, by SAS only
Not enough information
Decide whether enough information is given to prove 
that the triangles are congruent. 
Yes, congruent by SSS
Yes, congruent by SAS
Yes, congruent by AAS
​Yes, congruent by HL
​Yes, congruent by ASA
Not necessarily congruent
Decide whether enough information is given to prove 
that the triangles are congruent. 
Yes, congruent by SSS
Yes, congruent by SAS
Yes, congruent by AAS
​Yes, congruent by HL
​Yes, congruent by ASA
Not necessarily congruent
Decide whether enough information is given to prove 
that the triangles are congruent. 
Yes, congruent by SSS
Yes, congruent by SAS
Yes, congruent by AAS
Yes, congruent by HL
​Yes, congruent by ASA
Not necessarily congruent
The triangles shown are congruent.  Complete the congruence statement and give the correct postulate.
ΔBCA ≅ Δ                   by 
The triangles shown are congruent.  Complete the congruence statement and give the correct postulate.
ΔTSR ≅ Δ                   by 
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