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Congruent Triangle Criteria Calculator

Online triangle congruence checker. Choose the corresponding sides/angles (SSS/SAS/ASA/AAS/HL) to decide whether two triangles are congruent and give the reason—ideal for geometry.

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SSS, SAS, ASA, AAS, HL prove congruence
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Choose the conditions given

📖 Tutorial | Congruent Triangles

1. Definition
Triangles that coincide are congruent; corresponding sides and angles are equal.
2. Formula & Notation
SSSThree sides
SASTwo sides, included angle
ASATwo angles, included side
AASTwo angles, a side
HLHypotenuse-leg (right)
3. Properties & Laws
  • SSS, SAS, ASA, AAS prove it;
  • HL for right triangles;
  • SSA and AAA do not;
  • Corresponding segments equal.
4. Steps
  1. Choose the given conditions;
  2. Click "Decide";
  3. Read the reason.
5. Worked Examples
Example: two sides and included angle equal.
Solution: congruent by SAS.
6. Common Pitfalls
The SAS angle must be included;
SSA does not work;
AAA only proves similarity.

❓ FAQ | Congruent Triangles

Which tests work?
SSS, SAS, ASA, AAS; HL for right triangles.
Why not SSA?
It can give two different triangles.
Does AAA prove congruence?
No, only similarity.
Corresponding sides and angles?
Equal.
When does HL apply?
Right triangles only.
How to order vertices?
Match corresponding vertices in order.