To complete the proof that $\triangle GHJ \cong \triangle EKJ$, we need to use the information given in the statements and reasons to identify the final congruence step.

Let's analyze the proof:

1. Given Information: We are given that:

   • $\angle EIK \cong \angle GJH$
   • $\overline{LG} \cong \overline{LE}$
   • $\overline{JK} \cong \overline{HI}$

2. Step-by-Step Analysis:

   • Steps 4 and 5 show that the segments $HJ = HI + IJ$ and $IK = HI + IJ$, which implies that $HJ = IK$.
   • Steps 6 and 7, with the use of substitution and the transitive property of equality, establish that $HJ = IK$.

3. Conclusion (Step 8):

   • With $\angle EIK \cong \angle GJH$, $\overline{LG} \cong \overline{LE}$, $\overline{JK} \cong \overline{HI}$, and now $HJ = IK$, we have two angles and a side in each triangle that are congruent.
   • By the ASA (Angle-Side-Angle) Congruence Postulate, $\triangle GHJ \cong \triangle EKJ$.

Therefore, the reason for Step 8 is ASA Congruence Postulate.

Would you like more details on any part of this proof?

Here are some related questions to expand your understanding:

1. What other congruence postulates could apply in similar problems, like SSS or SAS?
2. How would the proof change if different parts of the triangles were congruent?
3. Can we use the information given to prove any other relationships in the figure?
4. What is the significance of the transitive property in geometric proofs?
5. How does the ASA postulate differ from AAS (Angle-Angle-Side) in proving triangle congruence?

Tip: Always make sure each statement in a proof has a clear, corresponding reason. This practice strengthens the logical flow and ensures the proof is complete.