If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

Explanation

To prove that two lines are parallel when the bisectors of a pair of corresponding angles formed by a transversal are parallel, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Lines and Transversal**:
Let the two lines be \( p \) and \( q \), and let the transversal be \( t \). The transversal intersects the lines \( p \) and \( q \) at points \( A \) and \( B \) respectively.

2. **Label the Angles**:
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