用等式表示线段FE，FA，FD之间的数量关系，并证明. ---**Question Number:** 27 **Question Stem:** 如图, 在正方形 ABCD 的外侧作射线 AP, ∠BAP = α (0° < α < 45°), 作点 B 关于射线 AP 的对称点 E, 连接 DE 交 AP 于点 F, 连接 AE. Translation: As shown in the figure, outside the square ABCD, draw ray AP, ∠BAP = α (0° < α < 45°), construct point E, the reflection of point B across ray AP, connect DE intersecting AP at point F, connect AE. **Sub-questions:** (1) 依题意补全图形; Translation: (1) Complete the figure according to the problem statement; (2) 若 α = 20°, 则 ∠AFD = ________ °; Translation: (2) If α = 20°, then ∠AFD = ________ °; [Handwritten answer]: 45 (Below it, 75 is written and crossed out). (3) 用等式表示线段 FE, FA, FD 之间的数量关系, 并证明. Translation: (3) Express the quantitative relationship between line segments FE, FA, FD with an equation, and prove it. [Handwritten mark]: A mark is drawn next to (3). **Diagram Description:** * Type: Geometric figure. * Content: * A square ABCD with vertices labeled in counterclockwise order (A top-left, B bottom-left, C bottom-right, D top-right). A right angle symbol is shown at vertex A. * A ray AP originates from vertex A, extending upwards and to the left of side AB. * An angle ∠BAP is indicated and labeled with the variable α and a single arc. * A point E is shown to the left and slightly above B. * Ray AP intersects line segment DE at point F. * Line segments AE and DE are drawn. * Angle ∠EAP is indicated with a double arc. Due to E being the reflection of B across AP, ∠BAP = ∠EAP = α. The diagram uses a single arc for ∠BAP and a double arc for ∠EAP, which is inconsistent with them being equal, but the reflection property implies equality. Let's assume ∠BAP = ∠EAP = α based on the text. * Angle ∠ADF is indicated with a double arc, suggesting ∠ADF = ∠EAP = α. * A separate, simpler diagram below shows only the square ABCD and the ray AP originating from A, extending outside the square. This likely represents the initial setup before adding the other points and lines.