给我讲解---题目 如图, 在四棱锥 $P - ABCD$ 中, 平面 $ABCD \perp$ 平面 $PCD$, 底面 $ABCD$ 为正方形, 点 $E$, $F$ 分别为 $AD$, $PC$ 的中点, 设平面 $PCD \cap$ 平面 $PBE = l$. (1)求证: $BC \perp DF$; (2)求证: $DF \parallel l$; (3)若 $PD = 1$, $DC = PC = 2$, 请判断平面 $PAD$ 与平面 $ABCD$ 是否垂直? 若垂直, 请证明; 若不垂直, 说明理由. **Chart/Diagram Description:** * **Type:** Geometric figure - a pyramid (specifically, a quadrilateral pyramid). * **Main Elements:** * **Vertices:** Labeled points P, A, B, C, D. * **Edges:** * Solid lines: PA, PB, BC, CD, PC. * Dashed lines: AD, AB, PD, BD, AC, PE, BF, EF, PF, DE. * **Base:** A quadrilateral ABCD (described as a square in the text). * **Apex:** Point P. * **Other points:** * E is labeled on edge AD, indicated as the midpoint of AD in the text. * F is labeled on edge PC, indicated as the midpoint of PC in the text. * **Planes:** The pyramid is formed by the base plane ABCD and faces PAB, PBC, PCD, PDA. The problem mentions planes ABCD, PCD, and PBE. * **Lines:** The line segment l is described as the intersection of plane PCD and plane PBE. Line segments like DF, PE, BF, EF, PF are also drawn. * **Relative Position:** Point P is above the base ABCD. Points E and F are midpoints of AD and PC, respectively. The figure shows the perspective view of the pyramid.