![]() The statement is often used as a justification in elementary geometry proofs when a conclusion of the congruence of parts of two triangles is needed after the congruence of the triangles has been established. If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as: Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure. ![]() Specifying two sides and an adjacent angle (SSA), however, can yield two distinct possible triangles. The shape of a triangle is determined up to congruence by specifying two sides and the angle between them (SAS), two angles and the side between them (ASA) or two angles and a corresponding adjacent side (AAS). (Most definitions consider congruence to be a form of similarity, although a minority require that the objects have different sizes in order to qualify as similar.) The related concept of similarity applies if the objects have the same shape but do not necessarily have the same size. In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters, and areas. ![]()
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