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In the image, you are given a quadrilateral \( ABCD \) with diagonals intersecting at points, and asked to determine whether any line segments are parallel given the condition that \( m \angle 2 = m \angle 3 \).

Here’s the reasoning:

- The given condition \( m \angle 2 = m \angle 3 \) suggests that angles 2 and 3 are equal. These angles are formed by the diagonals of the quadrilateral. 
- In a quadrilateral, if two alternate interior angles are equal (which seems to be the case here), it suggests that the lines are parallel.

If angles 2 and 3 are equal, this indicates that the diagonals are acting as transversals, and line \( AB \) must be parallel to line \( DC \) by the Alternate Interior Angle Theorem.

Thus, the correct answer is:  
**\( AB \parallel DC \)**

### Follow-up Questions:
1. What are alternate interior angles, and how do they help in proving lines are parallel?
2. Can diagonals in a quadrilateral be used to prove other types of lines parallel?
3. If angle 2 were not equal to angle 3, could any parallel lines be deduced?
4. How would you prove that a quadrilateral is a parallelogram?
5. What conditions are necessary for both pairs of opposite sides to be parallel?

### Tip:
Always look for congruent angles or corresponding angles when trying to prove that lines are parallel, especially when transversals are involved!

Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. When m∠2 = m∠3.

Explore how the equality of angles formed by diagonals in a quadrilateral can be used to deduce parallel lines using the Alternate Interior Angle Theorem. Learn how angles 2 and 3 indicate that line AB is parallel to line DC. This problem is suitable for students in Grades 8-10.

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