生成这个题目的讲解---Here is the extracted content from the image: **Problem Description:** As shown in the figure, in triangle ABC, AB=BC, DE is perpendicular to AB at point E, DF is perpendicular to BC at point D, and intersects AC at point F. **Chart/Diagram Description:** * **Type:** Geometric figure (triangle with internal segments and right angles). * **Main Elements:** * **Shape:** A triangle labeled ABC. * **Vertices:** A (top), B (bottom-left), C (bottom-right). * **Points:** * Point E is located on side AB. * Point D is located on side BC. * Point F is located on side AC. * **Lines/Segments:** * The three sides of the triangle: AB, BC, AC. * A segment DE connects point D to point E. * A segment DF connects point D to point F. * **Angles/Perpendiculars:** * A right angle symbol is shown at point E, indicating that segment DE is perpendicular to segment AB (DE ⊥ AB). * A right angle symbol is shown at point D (on side BC), indicating that segment DF is perpendicular to segment BC (DF ⊥ BC). **Question (1):** If ∠AFD=155°, find the measure of ∠EDF. **Solution/Explanation for Question (1):** Solution: Since ∠AFD = 155°, Therefore, ∠DFC = 25°. Since DF ⊥ BC, DE ⊥ AB, Therefore, ∠FDC = ∠AED = 90°. Therefore, ∠C = 180° - 90° - 25° = 65°. Since AB = BC, Therefore, ∠A = ∠C = 65°. Therefore, ∠EDF = 360° - 65° - 155° - 90° = 50°. **Question (2):** If point F is the midpoint of AC, prove that ∠CFD = (1/2)∠B.