Triangle congruence postulates

Math

Definition

Triangle congruence postulates are rules that establish when two triangles are congruent (identical in shape and size) based on specific combinations of equal sides and angles. The main postulates are SSS, SAS, ASA, AAS, and HL (for right triangles).

Examples

  • If two triangles have all three pairs of sides equal (SSS), they are congruent
  • If two sides and the included angle of one triangle equal those of another (SAS), the triangles are congruent
  • The HL postulate applies only to right triangles: if the hypotenuse and one leg are equal, the triangles are congruent
Key Fact

The five congruence shortcuts: SSS, SAS, ASA, AAS, and HL (right triangles only)

Related Terms

Cpctc Two-column proofs Isosceles triangle theorem Triangles

Study This Concept

Practice triangle congruence postulates with free review games in these units:

Geometry Unit 4: Congruent Triangles