Based on the image you uploaded, we are given that $\angle 1 \cong \angle 8$, and we need to determine which lines are parallel using a theorem or postulate.

In this case, $\angle 1$ and $\angle 8$ are corresponding angles. According to the Corresponding Angles Postulate, if two corresponding angles are congruent, then the lines cut by the transversal are parallel.

• The lines $k$ and $m$ are cut by the transversal $a$, and since $\angle 1 \cong \angle 8$, we conclude that $k \parallel m$ by the Corresponding Angles Postulate.

Would you like any further clarification or details on this?

Here are 5 related questions you might find interesting:

1. What are other types of angle pairs that can indicate parallel lines?
2. How does the Alternate Interior Angles Theorem relate to this problem?
3. Can we determine the parallelism of other lines based on the diagram?
4. What is the significance of transversal lines in geometry?
5. How does the Consecutive Interior Angles Theorem apply to parallel lines?

Tip: When two lines are parallel, all corresponding angles formed by a transversal are congruent, which is a helpful shortcut in geometry problems!