On a generalization of criteria A and D for congruence of triangles

The conditions determining that two triangles are congruent play a basic role in planimetry. By comparing not congruent triangles with respect to given sets of corresponding elements it is important to discover if they have any common geometric properties characterizing them. The present paper is devoted to an answer of this question. We give a generalization of criteria A and D for congruence of triangles and apply it to prove some selected geometric problems.