帮我解这道题目---Here is the extraction of the content from the image: **Question Number:** 27 **Text Description:** 如图，在四边形 ABCD 中，∠ABD = ∠ADB，CB ⊥ BD 于 B，AF ⊥ BD 于 F，CB = AF，AF 的延长线交 CD 于 E. **Diagram Description:** Type: Geometric figure Main Elements: * Points: A, B, C, D, E, F are labeled. * Lines/Segments: Segments AB, AD, BD, CD, BC are drawn. AF is drawn from A to BD, intersecting at F. AF is extended to E, where it intersects CD. * Angles: There is a right angle marked at B (∠CBD or ∠ABC could potentially be shown as right angles based on the text CB ⊥ BD at B). There is a right angle marked at F on BD (∠AFB or ∠AFD could be shown as right angles based on the text AF ⊥ BD at F). An angle marker indicates ∠ABD and ∠ADB are equal. * Relative Position: A is above BD. F is on BD, between B and D. C is below B and to the left of CD. E is on CD, and is the intersection of the extension of AF with CD. B is to the left of F, and F is to the left of D. **Problem Parts:** (1) 求证: EF = (1/2) AF; (2) 过点 A 作 GA ⊥ AD, 交 BD 于 G, 以 G 为圆心, BG 长为半径作弧, 交 AB 于 H, 连接 HD. ① 依题意补全图形; ② 用等式表示 EF 与 HD 之间的数量关系, 并证明.