If two parallel lines are intersected by a transversal then prove that the bisectors of any pair of alternate interior angles are parallel.

Explanation

To prove that the bisectors of any pair of alternate interior angles formed by two parallel lines intersected by a transversal are parallel, we can follow these steps:

### Step-by-Step Solution:

1. **Draw the Figure**:
- Let lines AB and CD be two parallel lines, and let XY be the transversal that intersects them.
- Mark the points of intersection as follows: let point E be the intersection of line XY with line AB and point F be the intersection of line XY with line CD.

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