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Let's work through the provided proof.

The given problem states that if a pair of corresponding angles formed by a transversal of two lines is congruent, then the two lines are parallel.

### Given:
- Line \( n \) is a transversal of line \( l \) and line \( m \).
- \(\angle a\) and \(\angle b\) are congruent corresponding angles. That is, \(\angle a = \angle b\).

### To Prove:
- Line \( l \parallel m \).

### Proof:
1. \(\angle a + \angle c = 180^\circ\) (angles in a linear pair)  
   Linear pairs of angles always add up to 180 degrees.

2. \(\angle a = \angle b\) (given)

3. So, \(\angle b + \angle c = 180^\circ\).

4. \(\angle b\) and \(\angle c\) are interior angles on the same side of the transversal.

5. Since the sum of these two angles equals 180 degrees, it proves that lines \( l \) and \( m \) are parallel by the **consecutive interior angles theorem**.

6. Thus, line \( l \parallel m \).

Finally, this property is called the **corresponding angles test** for parallel lines.

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If you need further details, feel free to ask! 

### Related Questions:
1. What are alternate interior angles and how do they prove lines are parallel?
2. How can we apply the converse of the corresponding angles theorem?
3. What other theorems relate to angles formed by a transversal?
4. How are co-interior angles used to prove lines parallel?
5. How do we distinguish between different angle pairs formed by a transversal?

**Tip:** Always remember, corresponding angles are on the same side of the transversal and in the same relative position.

If a pair of corresponding angles formed by a transversal of two lines is congruent, prove that the two lines are parallel.

Learn how to prove that two lines are parallel using the corresponding angles theorem. This problem covers key geometric concepts involving transversals and angle pairs, and includes a detailed step-by-step proof. Suitable for students in Grades 7-9.

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