1. **Problem statement:** Given rectangle ABCD with AB > BC, line xy passes through B and is parallel to diagonal AC. Line xy intersects AD at point E. Prove that quadrilateral ACBE is a parallelogram. 2. **Recall properties:** In a rectangle, opposite sides are equal and parallel, and diagonals are equal. 3. **Step 1:** Since ABCD is a rectangle, AB \parallel DC and AD \parallel BC. 4. **Step 2:** Diagonal AC connects vertices A and C. 5. **Step 3:** Line xy passes through B and is parallel to AC by given. 6. **Step 4:** Since xy \parallel AC and xy passes through B, and xy intersects AD at E, then E lies on AD. 7. **Step 5:** Consider quadrilateral ACBE with vertices A, C, B, E. 8. **Step 6:** Since xy \parallel AC and passes through B and E, segment BE \parallel AC. 9. **Step 7:** In rectangle ABCD, AD \parallel BC, so segment AE \parallel BC. 10. **Step 8:** Since AB \parallel DC and ABCD is rectangle, AB \parallel DC and AB = DC. 11. **Step 9:** By construction, BE \parallel AC and AE \parallel BC, so opposite sides of quadrilateral ACBE are parallel. 12. **Conclusion:** Quadrilateral ACBE has both pairs of opposite sides parallel, so ACBE is a parallelogram. **Final answer:** Quadrilateral ACBE is a parallelogram because BE \parallel AC and AE \parallel BC, satisfying the definition of a parallelogram.