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    Congruent Triangles


    Two triangles are congruent if their corresponding sides and angles are equal. Usually it is sufficient to establish the equality of three corresponding parts and use one of the following results to conclude the congruence of the two triangles.

    SAS, SSS, ASA, and AAS

    SAS (Side-Angle-Side): Two triangles are congruent if two sides and included angle of one triangle are equal, respectively, to two sides and included angle of the other triangle.

    SSS (Side-Side-Side): Two triangles are congruent if three sides of one triangle are equal, respectively, to three sides of the other triangle.

    ASA (Angle-Side-Angle): Two triangles are congruent if two angles and included side of one triangle are equal, respectively, to two angles and included side of the other triangle.

     

    AAS (Angle-Angle-Side): Two triangles are congruent if a pair of corresponding angles and a not-included side of one triangle are equal, respectively, to corresponding angles and not-included side of the other triangle.