Yes, BD ≅ BD by the AAS (Angle-Angle-Side) congruence criterion. According to AAS, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, both triangles have the angle A (common), angle B (common), and the side BD (included). Therefore, the triangles must be congruent.
