Subjects geometry

Cube Edge 574Fbf

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1. **Problem statement:** Given a net of a cube with labeled edges, determine which edge joins with edge $X$ when the net is folded into a cube. 2. **Understanding the net:** The net consists of six squares arranged in a cross shape: - Top square has edge $X$ on its upper edge. - Left square has edge $F$ on its right edge. - Central square is unlabeled. - Right square has edge $A$ on its left edge. - Bottom right square has edge $B$ on its left edge. - Bottom center square has edges $D$ (upper edge) and $C$ (right edge). - Bottom left square has edge $E$ on its upper edge. 3. **Cube folding rules:** When folded, adjacent squares in the net become adjacent faces of the cube. Edges that are adjacent in the net will join in the cube. 4. **Identify adjacency of edge $X$:** Edge $X$ is on the upper edge of the top square. The top square is adjacent to the central square below it. 5. **Edges adjacent to $X$ in the net:** The top square's lower edge touches the central square's upper edge. The edge $X$ is on the top square's upper edge, which is not adjacent to any other square in the net. 6. **Folding the net:** When folded, the top square folds down to form one face of the cube. The edge $X$ will join with the edge on the square adjacent to the top square's upper edge in the folded cube. 7. **Determining the joined edge:** The top square's upper edge $X$ will join with the edge on the bottom square's upper edge when folded. The bottom center square has edge $D$ on its upper edge. 8. **Conclusion:** Edge $X$ joins with edge $D$ when the net is folded into a cube. **Final answer:** Edge $X$ joins with edge $D$.