1. **State the problem:** Given that lines $g$ and $h$ are parallel ($g \parallel h$) and that angle 6 is congruent to angle 4 ($\angle 6 \cong \angle 4$), prove that line $f$ is parallel to line $h$ ($f \parallel h$). 2. **Recall the relevant properties:** - When a transversal crosses parallel lines, corresponding angles are congruent. - If two lines are cut by a transversal and corresponding angles are congruent, then those two lines are parallel. 3. **Analyze the given information:** - Since $g \parallel h$, the transversal creates pairs of corresponding angles between $g$ and $h$. - $\angle 6$ and $\angle 4$ are congruent. 4. **Identify the transversal and angles:** - The transversal intersects lines $g$, $f$, and $h$ creating angles 1 through 8. - $\angle 6$ is formed between $f$ and $h$. - $\angle 4$ is formed between $g$ and $f$. 5. **Use the congruence of angles:** - Since $\angle 6 \cong \angle 4$, and $\angle 4$ corresponds to $\angle 6$ across line $f$, this implies that $f$ and $h$ are parallel by the Corresponding Angles Postulate. 6. **Conclusion:** - Therefore, $f \parallel h$. **Step 3 in the table:** The reason is the Corresponding Angles Postulate, which states that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.