1. **Problem Statement:** We need to explain why angles 2 and 3 are congruent. 2. **Given Information:** - \(\angle 1 \cong \angle 3\) - \(\angle 2 \cong \angle 4\) - \(\angle 1 \cong \angle 2\) - \(\angle 3 \cong \angle 4\) - \(\angle ABD\) and \(\angle CBE\) are right angles. - \(\angle ABC \cong \angle DBE\) 3. **Key Concept:** When two parallel lines are cut by a transversal, alternate interior angles are congruent. 4. **Explanation:** - Angles 2 and 3 are alternate interior angles formed by the transversal intersecting the two parallel lines. - By the Alternate Interior Angles Theorem, these angles are congruent. 5. **Conclusion:** - Therefore, \(\angle 2 \cong \angle 3\) because they are alternate interior angles formed by a transversal crossing parallel lines. 6. **Additional Note:** - Vertical angles are congruent, which supports the congruence of other angle pairs. - Right angles \(\angle ABD\) and \(\angle CBE\) confirm perpendicularity but are not directly related to angles 2 and 3 congruence. **Final answer:** \(\angle 2 \cong \angle 3\) by the Alternate Interior Angles Theorem.