Triangle Congruence Checker
Enter the known sides and angles of two triangles. The Triangle Congruence Checker will instantly tell you if they are congruent and which theorem applies.
Triangle A
Triangle B
About the Triangle Congruence Checker
The Triangle Congruence Checker is a scientifically accurate online tool that instantly determines whether two triangles are congruent using the five classical congruence theorems: SSS, SAS, ASA, AAS, and HL (for right triangles). This Triangle Congruence Checker implements rigorous geometric proofs as presented in standard textbooks (e.g., Moise, *Elementary Geometry from an Advanced Standpoint*, 1990) and is trusted by students, teachers, and mathematicians worldwide. Proudly supported by Agri Care Hub.
The Five Congruence Theorems
SAS – Two sides and the included angle equal
ASA – Two angles and the included side equal
AAS – Two angles and a non-included side equal
HL – Hypotenuse and one leg equal (right triangles only)
Why the Triangle Congruence Checker Matters
Congruence is one of the most fundamental concepts in Euclidean geometry. Proving triangles congruent allows us to conclude that all corresponding parts (sides and angles) are equal — a principle used daily in engineering, architecture, computer graphics, robotics, and countless real-world applications. Understanding exactly which theorem applies also deepens geometric reasoning skills and prepares students for advanced topics like similarity, trigonometry, and coordinate geometry proofs.
How to Use the Triangle Congruence Checker
- Enter the known sides and angles for Triangle A and Triangle B.
- You only need to fill in the values you know — leave unknown fields blank.
- Click “Check Triangle Congruence”.
- The tool instantly tells you if the triangles are congruent and which theorem proves it.
When Should You Use This Tool?
- High-school and college geometry homework
- Preparing for standardized tests (SAT, ACT, GCSE, IB)
- Teaching demonstrations and classroom activities
- Verifying geometric proofs in engineering or design work
- Self-study and competitive math preparation
Scientific Foundation
All five congruence postulates were rigorously proven within Euclidean geometry centuries ago and remain unchallenged in standard plane geometry. The SSS, SAS, and ASA postulates are accepted as axioms or proven from Hilbert’s foundations. AAS follows from ASA and the angle-sum theorem, while HL is proven using Pythagoras and SSS. For full proofs and history, see the Wikipedia article on Triangle Congruence.
Limitations
The checker assumes Euclidean (flat) geometry and works only with triangles (3 sides). It does not handle SSA (ambiguous case) as a congruence theorem — SSA can produce zero, one, or two triangles and is therefore not sufficient for congruence.
Conclusion
The Triangle Congruence Checker brings centuries of geometric certainty into an instant, user-friendly tool. Whether you’re a student mastering proofs, a teacher explaining theorems, or a professional verifying designs, this checker delivers mathematically perfect results every time. For more educational tools, visit Agri Care Hub.