Question: Given: $HF \parallel JK$; $HG \cong JG$ Prove: Triangle $FHG \cong$ Triangle $KJG$ Triangles $FHG$ and $KJG$ connect at point $G$. Sides $FH$ and $JK$ are parallel. Sides $HG$ and $GJ$ are congruent. To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof? $\text{Angle } FGH \cong \text{Angle } KGJ$ because vertical angles are congruent. $\text{Angle } JKG \cong \text{Angle } HFG$ because vertical angles are congruent. $\text{Angle } FHG \cong \text{Angle } JKG$ because right angles are congruent. $\text{Angle } HFG \cong \text{Angle } KJG$ because alternate interior angles are congruent.

1. **State the problem:** We are given that $HF \parallel JK$ and $HG \cong JG$. We need to prove that $\triangle FHG \cong \triangle KJG$ by ASA (Angle-Side-Angle) congruence. 2. **Identify given information and what to prove:** - $HF \parallel JK$ (given) - $HG \cong JG$ (given) - Triangles share vertex $G$ 3. **Recall ASA congruence rule:** Two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. 4. **Analyze angles:** Since $HF \parallel JK$ and $HG$ and $JG$ are transversal segments, - $\angle HFG \cong \angle KJG$ because they are alternate interior angles formed by the parallel lines $HF$ and $JK$ and transversal $FG/GJ$. 5. **Side congruence:** $HG \cong JG$ is given. 6. **Vertical angles:** $\angle FGH \cong \angle KGJ$ because vertical angles formed by intersecting lines at $G$ are congruent. 7. **Apply ASA:** We have two pairs of angles congruent ($\angle HFG \cong \angle KJG$ and $\angle FGH \cong \angle KGJ$) and the included side $HG \cong JG$. 8. **Conclusion:** Therefore, by ASA, $\triangle FHG \cong \triangle KJG$. **Answer to the question:** The statement and reason that could be used as part of the proof is: $\boxed{\text{Angle } HFG \cong \text{Angle } KJG \text{ because alternate interior angles are congruent.}}$