用高一数学知识给我讲一下13题---四、解答题: 本题共 3 小题, 共 40 分. 解答应写出文字说明、证明过程及演算步骤. 13.(本小题满分 12 分) 如图, 四棱锥 P-ABCD 的底面是正方形, PD ⊥ 底面 ABCD, 点 E 在棱 PB 上. (1)求证: 平面 AEC ⊥ 平面 PDB; (2)当 PD = √2 AB, 且 E 为 PB 的中点时, 求 AE 与平面 PDB 所成的角的大小. (13. 题图) 图示描述: 类型: 三维几何图形 (四棱锥) 主要元素: * 点: P (apex), A, B, C, D (base vertices), E (on edge PB). * 线: * 实线: PA, PB, PC, AB, BC, AE, EC. These represent visible edges and lines. * 虚线: PD, AD, CD, DB. These represent hidden edges or lines within planes. PD is a vertical line from P to D. DB is a diagonal of the base. * 形状: * 四棱锥 P-ABCD. * 底面 ABCD 描述为正方形 (in the text, shown as a parallelogram in perspective). * 相对位置和方向: * P is the apex, ABCD is the base. * PD is perpendicular to the base ABCD. * E is a point on the edge PB. * The figure shows plane AEC (formed by lines AE, EC, AC) and plane PDB (formed by lines PD, DB, PB). * 标注: Points A, B, C, D, P, E are labeled. The figure is labeled as "(13. 题图)". 高一数学试题 第 3 页 (共 4 页)