用中文证明这道题目，给出完整严谨的证明过程，这是初二的数学题---**Given:** 如图, 在四边形 ABCD 中, AD=BC, M、N 分别是 AB、CD 的中点, AD、BC 的延长线交 MN 于 E、F. (As shown in the figure, in quadrilateral ABCD, AD=BC, M and N are the midpoints of AB and CD respectively, the extensions of AD and BC intersect MN at E and F.) **To prove:** ∠DEN = ∠F. **Diagram Description:** * **Type:** Geometric figure. * **Main Elements:** * Points: A, B, C, D are the vertices of a quadrilateral. M is the midpoint of AB. N is the midpoint of CD. E is a point on the extension of AD. F is a point on the extension of BC. * Lines: Line segments AD, AB, BC, CD form the quadrilateral. A line segment connects M and N. The line passing through AD is extended beyond D to intersect the line passing through M and N at E. The line passing through BC is extended beyond C to intersect the line passing through M and N at F. * Labels: Points are labeled A, B, C, D, M, N, E, F.