Final answer:
The sufficient information to conclude that the two triangles are congruent is option D: FG = JK.
Step-by-step explanation:
For two triangles to be congruent, three sides and three angles must be equal in measurement between the two triangles (by the SSS, SAS, ASA, AAS, or HL congruence theorems). In this case, the information that FG = JK indicates that two corresponding sides of the triangles are equal. If the two triangles share another pair of equal sides or an angle that matches exactly (without ambiguity), it would suffice to prove their congruence definitively. However, knowing FG = JK alone is insufficient to conclude congruence definitively, as it's only one pair of sides.
If additional information were provided, such as the equality of another pair of sides or an angle, it could contribute to proving the congruence of the triangles. For instance, if another pair of sides or an angle were equal (like FG = JK and LK = GH), or if an angle was specified to be congruent between the two triangles (such as ∠F = ∠J), this would be adequate to establish their congruence based on corresponding sides and angles.
Therefore, while FG = JK provides valuable information, by itself, it isn't enough to conclude definitively that the triangles are congruent. More information about other sides or angles needs to be provided to substantiate their congruence.