给出这道题的完整解题过程---Here is the extracted content from the image: **Question Source:** 1. (2009 全国卷 I) **Question Stem:** 如图, 四棱锥 S-ABCD 中, 底面 ABCD 为矩形, SD ⊥ 底面 ABCD, AD = √2, DC = SD = 2, 点 M 在侧棱 SC 上, ∠ABM = 60°. **Sub-questions:** (I) 证明: M 是侧棱 SC 的中点; (II) 求二面角 S-AM-B 的大小。 **Chart/Diagram Description:** * **Type:** Three-dimensional geometric figure, specifically a rectangular pyramid. * **Main Elements:** * **Vertices:** Labeled S (apex), A, B, C, D (base vertices), and M (a point on the edge SC). * **Lines/Edges:** * Solid lines represent visible edges: SA, SB, SC, AB, BC, CD, BM, AM. * Dashed lines represent hidden edges: SD, AD, DC. * **Shapes:** * The base ABCD is a rectangle, shown in perspective. * The pyramid has four triangular lateral faces: △SAB, △SBC, △SCD, △SDA. * Lines AM and BM are drawn, forming a triangle △AMB within the pyramid. * **Relative Position and Direction:** * Point S is the apex of the pyramid. * Points A, B, C, D form the rectangular base. * Edge SD is perpendicular to the base ABCD (indicated by SD being a vertical dashed line from S to D). * Point M lies on the edge SC.