https://file.aiquickdraw.com/mathbot/file/1727466114759g3g5ou2q.jpg

In the provided image, we are asked to determine the relationship between ∠1 and ∠5 based on the given diagram of parallel lines and a transversal.

- The two lines \( l \) and \( m \) are parallel (\( l \parallel m \)).
- Line \( t \) is the transversal intersecting the two parallel lines.

∠1 and ∠5 are positioned such that:
- They are on the same side of the transversal \( t \).
- ∠1 is located above line \( l \) and ∠5 is located below line \( m \).

This means ∠1 and ∠5 are **corresponding angles**. In geometry, corresponding angles formed by a transversal with two parallel lines are always congruent.

Thus, the correct answer is **congruent**.

Would you like more details on this, or do you have any further questions?

Here are 5 related questions to deepen your understanding:
1. What are alternate interior angles, and how do they relate to parallel lines?
2. Can corresponding angles ever be non-congruent? Why or why not?
3. What is the difference between same-side interior and same-side exterior angles?
4. How do vertical angles differ from corresponding angles in terms of their positioning?
5. What geometric theorem guarantees that corresponding angles are congruent?

**Tip:** When identifying angle relationships, focus on the transversal and parallel lines to determine if they are corresponding, alternate, or same-side angles.

Explore how ∠1 and ∠5 are congruent corresponding angles formed by a transversal intersecting two parallel lines. This geometry problem is designed for students in Grades 7-9, focusing on angle relationships with parallel lines and transversals.

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