生成讲解视频---**Extracted Content:** **Question Stem:** 已知: 点 A, C, B, D 在同一条直线, AC = BD, ∠M = ∠N = 90°, AM = CN. 求证: MB//ND. **Translated Question Stem:** Given: Points A, C, B, D are on the same straight line, AC = BD, ∠M = ∠N = 90°, AM = CN. Prove: MB//ND. **Mathematical Information:** * **Given Conditions:** * Points A, C, B, D are collinear. * AC = BD * ∠M = 90° (interpreted as ∠AMB = 90° for triangle AMB) * ∠N = 90° (interpreted as ∠CND = 90° for triangle CND) * AM = CN * **To Prove:** * MB // ND **Chart/Diagram Description:** * **Type:** Geometric Figure. * **Main Elements:** * **Points:** There are six labeled points: A, C, B, D, M, N. * **Lines/Segments:** * A straight horizontal line segment contains points A, C, B, D, ordered from left to right as A, then C, then B, then D. * Two triangles are drawn: * Triangle AMB, formed by connecting points A, M, and B with straight line segments (AM, MB, AB). * Triangle CND, formed by connecting points C, N, and D with straight line segments (CN, ND, CD). * **Shapes:** Two distinct triangles, ΔAMB and ΔCND. * **Angles:** Based on the problem statement (∠M = ∠N = 90°), it is implied that ΔAMB is a right-angled triangle with the right angle at vertex M (∠AMB = 90°), and ΔCND is a right-angled triangle with the right angle at vertex N (∠CND = 90°). * **Labels and Annotations:** All vertices and points on the line are clearly labeled with capital letters (A, C, B, D, M, N). * **Relative Position and Direction:** * Points A, C, B, D are collinear on a horizontal line. * Point M is positioned above the line containing A, C, B, D. * Point N is positioned above the line containing A, C, B, D, to the right of M. * The two triangles, ΔAMB and ΔCND, are positioned such that they appear to overlap. Specifically, the segment MB of ΔAMB intersects the segment CN of ΔCND.