Final answer:
The geometry problem requires proving that two triangles are congruent. However, the information provided is not sufficient to conclusively prove congruence using standard theorems like ASA or AAS.
Step-by-step explanation:
The question appears to be a problem from the field of mathematics, specifically dealing with geometry, and centers around proving the congruence of two triangles.
To prove that triangles FGH and LGK are congruent, we would typically look for congruence theorems such as Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS). The given information that FH is parallel to LK and GF is congruent to GL could suggest that corresponding angles are equal, which is a step towards proving the triangles are congruent via ASA or AAS. However, the information provided seems insufficient to definitively prove the congruence of triangles FGH and LGK without additional statements or diagrams to indicate the congruency of sides or angles.