题目如图片，请解答这道初二数学平行四边形求证等综合题---**Extraction Content:** **Question 25 (14 points)** **Question Stem:** 如图, 在平面直角坐标系中, A(2, 6), B(4, 0), 将△AOB绕点B旋转, 使得点O落在AO边上点C处, 点A落在点D处, 连接AD. **Sub-questions:** (1) 求证: 四边形 AOBD 是平行四边形; (2) 直线 y = kx - 3k + 3 过点 C, 且与线段 BD 交于点 E, 求证: AC = BE; (3) 点 M 是直线 CD 上一动点, 在 x 轴上是否存在点 N, 使以 A、B、M、N 为顶点的四边形是平行四边形? 若存在, 请直接写出点 N 的坐标; 若不存在, 请说明理由. **Mathematical Formulas/Equations:** Line equation: y = kx - 3k + 3 **Diagram Description:** Type: Coordinate system with plotted points and lines forming geometric shapes. Main Elements: - Coordinate Axes: X-axis (horizontal, labeled 'x'), Y-axis (vertical, labeled 'y'). - Origin: Point O at the intersection of the axes. - Points: O, A, B, C, D are labeled. Point A is at coordinates (2, 6). Point B is at coordinates (4, 0). Point C is on the line segment OA. Point D is the rotation of A around B. - Lines/Segments: Lines connecting O-A, O-B, A-B, A-D, B-D, C-D. Line segment BD is drawn. Line segment OA is drawn, with C on it. - Shapes: Quadrilateral AOBD is formed by points A, O, B, D. Triangle AOB is implied by the rotation description. - Labels: Points O, A, B, C, D are labeled. The diagrams are labeled "备用图1" and "备用图2" (Auxiliary Diagram 1 and Auxiliary Diagram 2). The first diagram is not explicitly labeled but shows the setup. **Other Relevant Text:** None beyond the question stem and sub-questions.