Geometry — Congruence
GradesGeometry & FunctionsGeometry — CongruenceTriangle Congruence Criteria

Triangle Congruence Criteria

🔷 Geometry — Congruence
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Triangle Congruence Criteria

Prove triangles congruent using SSS, SAS, ASA, and AAS.

Two triangles are congruent if all corresponding sides and angles are equal. However, we do not need to verify all six parts. The triangle congruence postulates give us minimal sets of conditions that guarantee congruence.

Triangle Congruence Criteria

SSS: three pairs of equal sidesSAS: two sides and the included angleASA: two angles and the included sideAAS: two angles and a non-included sideHL: hypotenuse and one leg (right triangles only)

Note: SSA (side-side-angle) does NOT guarantee congruence — it is the "ambiguous case."

△ABC≅△DEF  ⟹  AB=DE,  BC=EF,  AC=DF,  ∠A=∠D,  ∠B=∠E,  ∠C=∠F\triangle ABC \cong \triangle DEF \implies AB = DE,\; BC = EF,\; AC = DF,\; \angle A = \angle D,\; \angle B = \angle E,\; \angle C = \angle F
📝Writing a Congruence Proof
Given: AB = DE and ∠B = ∠E and BC = EF. The included angle ∠B is between sides AB and BC. This matches SAS, so △ABC ≅ △DEF by SAS.
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Remember This!

"Included" means between the two sides (for SAS) or between the two angles (for ASA). Always identify what is "included" before citing a criterion.

✏️ Try It!

Two triangles share two pairs of equal angles and the side between those angles is equal. What criterion proves them congruent?

Take Quiz 📝 — 25 Questions