Question

$\overleftrightarrow{gj}$ bisects $\angle hgi$ and $\overline{gi} \cong \overline{gh}$. complete the proof that $\triangle ghj \cong \triangle gij$.

Explanation:

Step1: List given congruent sides

$\overline{GI} \cong \overline{GH}$ (Given)

Step2: List bisector-created congruent angles

$\angle HGJ \cong \angle IGJ$ (Angle bisector definition)

Step3: Identify common side

$\overline{GJ} \cong \overline{GJ}$ (Reflexive Property)

Step4: Apply SAS congruence

By SAS (Side-Angle-Side) Congruence Postulate, $\Delta GHJ \cong \Delta GIJ$

To complete the proof table, the 4th statement and reason are:
Statement 4: $\overline{GJ} \cong \overline{GJ}$
Reason 4: Reflexive Property of Congruence
Then the final statement (added line):
Statement 5: $\Delta GHJ \cong \Delta GIJ$
Reason 5: SAS Congruence Postulate

Answer:

$\Delta GHJ \cong \Delta GIJ$