1. **Problem statement:** Count how many pairs of lines (edges) in the cuboid can intersect when extended in 3D. 2. **Understanding the cuboid edges:** The cuboid has 12 edges connecting vertices: - Bottom face: A-B, B-C, C-D, D-A - Top face: I-F, F-G, G-H, H-I - Vertical edges: A-I, B-F, C-G, D-H 3. **Types of possible line intersections:** - Edges sharing a vertex obviously intersect. - Parallel edges do not intersect (considering lines as infinite, some may). - Skew edges (non-parallel, non-intersecting lines in 3D) do not intersect. 4. **Checking intersecting edges:** - Each vertex is shared by three edges; those intersect at the vertex. - Each vertical edge intersects exactly with the top and bottom edges connected to its vertices. - No edge crosses the interior of another edge without sharing a vertex. 5. **Counting intersections at vertices:** - Total vertices = 8 - Each vertex has 3 edges meeting - Number of edge pairs intersecting at each vertex = \(\binom{3}{2} = 3\) - Total intersecting pairs at vertices = \(8 \times 3 = 24\) 6. **Checking for intersections not at vertices (line crossings):** - In a cuboid, edges do not cross each other except at vertices. 7. **Final answer:** The only line intersections occur at vertices, with a total of 24 pairs of edges intersecting. **Answer:** There are \textbf{24} pairs of edges that intersect (meet) in the cuboid.