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

Congruence Case

Triangle 1 — sides

a₁

b₁

c₁

Triangle 2 — sides

a₂

b₂

c₂

Triangle 1 — two sides + included angle

a₁

∠C₁ (°)

b₁

Triangle 2 — two sides + included angle

a₂

∠C₂ (°)

b₂

Triangle 1 — angle, side, angle

∠A₁ (°)

side b₁

∠C₁ (°)

Triangle 2 — angle, side, angle

∠A₂ (°)

side b₂

∠C₂ (°)

Triangle 1 — two angles + non-included side

∠A₁ (°)

∠B₁ (°)

side c₁

Triangle 2 — two angles + non-included side

∠A₂ (°)

∠B₂ (°)

side c₂

Triangle 1 — hypotenuse & leg (right triangle)

Hypotenuse h₁

Leg l₁

Triangle 2 — hypotenuse & leg (right triangle)

Hypotenuse h₂

Leg l₂

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.

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