Geometry Intermediate

Triangle Congruence — SSS, SAS, ASA, AAS, HL

Select a congruence postulate, enter the required measurements for both triangles, and the calculator checks whether the triangles are congruent.

5 congruence cases
Step-by-step reasoning
Side-by-side diagram
Input
Triangle 1 — sides
Triangle 2 — sides
Triangle 1 — two sides + included angle
Triangle 2 — two sides + included angle
Triangle 1 — angle, side, angle
Triangle 2 — angle, side, angle
Triangle 1 — two angles + non-included side
Triangle 2 — two angles + non-included side
Triangle 1 — hypotenuse & leg (right triangle)
Triangle 2 — hypotenuse & leg (right triangle)
Congruence Check
Select a case and enter measurements.
Step-by-Step Reasoning
Triangle Comparison
Congruence Postulates

SSS: All three pairs of sides equal.

SAS: Two sides and the angle between them equal.

ASA: Two angles and the included side equal.

AAS: Two angles and a non-included side equal.

HL: Hypotenuse and one leg of right triangles equal.

Why Not SSA or AAA?

SSA is not a valid congruence postulate — two triangles can have the same SSA information but different shapes (the ambiguous case).

AAA only guarantees similarity, not congruence. The triangles could be different sizes.

Related Calculators
Triangle Area
Multiple methods for computing triangle area.
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Pythagorean Theorem
Find missing sides, including for HL.
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Angle Relationships
Complementary, supplementary, and vertical angles.
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All Calculators
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Put It Into Practice

The calculator shows the steps — a quiz proves you can do them on your own.

Geometry Practice Quizzes →
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