1. **Problem statement:** Given a rectangular prism ABCD.A'B'C'D', a plane parallel to the side ABB'A' intersects edges AD, BC, A'D', B'C' at points M, N, M', N' respectively. Prove that the quadrilateral ABNM.A'B'N'M' is a rectangular prism. 2. **Key concepts and formulas:** - A rectangular prism (hình hộp) is a parallelepiped with all faces rectangles. - If a plane is parallel to a face of a prism, the intersection with the prism forms a smaller prism similar to the original. - Parallelism and congruence of edges are crucial. 3. **Step-by-step proof:** 1. Since the plane is parallel to the face ABB'A', it is parallel to the edges AB and BB'. 2. Points M and N lie on edges AD and BC respectively, which are parallel and equal in length. 3. Points M' and N' lie on edges A'D' and B'C' respectively, which are parallel and equal in length. 4. Because the plane is parallel to ABB'A', the segments MN and M'N' are parallel to AB and A'B' respectively. 5. Quadrilateral ABNM lies in the bottom base ABCD, and A'B'N'M' lies in the top base A'B'C'D'. 6. Edges AB and A'B' are parallel and equal, and similarly MN and M'N' are parallel and equal. 7. The quadrilateral ABNM.A'B'N'M' has all faces parallelograms with right angles, so it is a rectangular prism. 4. **Conclusion:** Thus, ABNM.A'B'N'M' is a rectangular prism.