A net of a cube and a schematic diagram of the cube are shown in the figure. (1) Mark the letters $F , G , H$ at the corresponding vertices of the cube (no explanation needed); (2) Determine the positional relationship between plane $B E G$ and plane $A C H$, and prove your conclusion; (3) Prove: line $D F \perp$ plane $B E G$. [Figure][Figure]
\section*{18. (This question is worth 12 points)}
A net of a cube and a schematic diagram of the cube are shown in the figure. (1) Mark the letters $F , G , H$ at the corresponding vertices of the cube (no explanation needed); (2) Determine the positional relationship between plane $B E G$ and plane $A C H$, and prove your conclusion; (3) Prove: line $D F \perp$ plane $B E G$.\\
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\includegraphics[max width=\textwidth, alt={}, center]{2d3697d8-6dcb-4d1f-9701-cbe4cd401b55-3_572_574_1665_1446}