讲解图片中题目---**万唯原创 问题提出** (1) 如图①, 在 Rt△ABC 中, ∠B=90°, ∠A=30°, E 为 BC 的中点, D,F 分别为 AB,AC 上任意一点, 连接 DE,DF, 若 BC=2, 求 DE+DF 的最小值; 问题解决 (2) 某市为进一步完善排水防涝应急机制, 做好城市排水防涝应急管理工作, 准备对部分地下管道进行加固扩建, 如图②, 矩形 ABCD 为某市地下管网部分示意图, 工作人员在原管道 BD 上取一点 E, 新修主管道 AE, 为增加分流效果, 在 AE 上取中点 F, 在 CD 上取一点 G, 新修建分流管道 BG,FG, 经测量 ∠BDC=30°, AD=2 000 米, 若新修分流管道的费用为 500 元/米, 问本次新修分流管道至少花费多少元? (本题涉及微专题见本书 P125) --- **Chart/Diagram Description:** **图①:** * Type: Geometric figure (Right-angled triangle). * Main Elements: * Vertices: A, B, C. * Points: D is on line segment AB. F is on line segment AC. E is on line segment BC. * Lines: Line segments AB, BC, AC forming triangle ABC. Line segments DE and DF. * Angles: Triangle ABC is a right-angled triangle at B (∠B=90° as per text, though not marked with a square). Angle A is labeled. * Labels: Points A, B, C, D, E, F are labeled. "图①" is below the figure. * Relative Position: Vertices A, B, C form a triangle. D is on the left side segment AB. E is on the bottom segment BC. F is on the right side segment AC. DE and DF connect these points. **图②:** * Type: Geometric figure (Rectangle). * Main Elements: * Vertices: A, B, C, D. * Points: E is on the diagonal BD. F is on the line segment AE. G is on the line segment CD. * Lines: Line segments AB, BC, CD, AD form rectangle ABCD. Diagonal BD. Line segment AE. Line segments BG and FG. * Labels: Points A, B, C, D, E, F, G are labeled. "图②" is below the figure. * Relative Position: Vertices A, B, C, D form a rectangle in clockwise order starting from top-left. E is on the diagonal BD. F is on AE. G is on CD. BG and FG connect points B and G, and F and G respectively.