Prove triangle congruence using SSS, SAS, ASA, and AAS theorems.
Select Theorem
Theorem Details
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Required Match
Side 1, Side 2, Side 3
Proof Visualization
A
B
C
D
E
F
△ABC ≅ △DEF
Proved by SSS
About this calculator
Quick Reference
CPCTCCorresponding Parts of Congruent Triangles are Congruent
AAASimilarity only
SSAAmbiguous (Not a proof)
What is Congruence?
Two triangles are congruent if they are identical in shape and size. This means all corresponding sides and all corresponding angles are equal. However, we only need three specific pieces of information to prove congruence.
💡
Pro Tips
SSS (Side-Side-Side): All three sides are equal.
SAS (Side-Angle-Side): Two sides and the included angle are equal.
ASA (Angle-Side-Angle): Two angles and the included side are equal.
AAA is NOT a congruence theorem (only proves similarity).
!
Fun Facts
"Congruent comes from the Latin word 'congruere', which means 'to agree'."
"Rigid transformations (rotation, translation, reflection) always result in congruent shapes."
"The 'HL' (Hypotenuse-Leg) theorem is a special congruence rule for right triangles."
