Triangle Congruence Calculator
Check if two triangles are congruent or similar using SSS, SAS, ASA, and AAS criteria with step-by-step geometry proofs.
What Is Triangle Congruence?
Two triangles are congruent when they have the same shape and size. Every corresponding side and angle matches. Congruence is stronger than similarity: similar triangles share shape but may differ in scale.
Related tools: Similar Triangles Calculator, SSS Triangle Calculator, and Triangle Calculator.
Four Congruence Postulates
- SSS: All three corresponding sides are equal.
- SAS: Two sides and the included angle are equal.
- ASA: Two angles and the included side are equal.
- AAS: Two angles and a non-included side are equal.
Worked Example (SSS)
Triangle 1 has sides 5, 6, 7. Triangle 2 also has sides 5, 6, 7. The sorted side lists match, so the triangles are congruent by SSS.
Frequently Asked Questions
What is the difference between congruent and similar triangles?
Congruent triangles are identical in size and shape. Similar triangles have equal angles and proportional sides but may be scaled differently.
Is SSA enough for congruence?
No. SSA (two sides and a non-included angle) can produce two different triangles, so it is not a valid congruence test.
Is AAS the same as ASA?
Yes. AAS and ASA describe the same congruence condition with different labeling of the known side.
Are AAA triangles congruent?
No. AAA only fixes shape, not size. Triangles with the same three angles are similar, not necessarily congruent.
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