解图片中的试题---**Question 1:** **Question Stem:** 1. 如图, 矩形ABCD中, E为BC上一点, DF⊥AE于F. (1) 求证: △ABE∽△DFA; (2) 若AB=3, AD=6, BE=4, 求DF的长. **Translation of Question Stem:** 1. As shown in the figure, in rectangle ABCD, E is a point on BC, DF⊥AE at F. (1) Prove that: △ABE∽△DFA; (2) If AB=3, AD=6, BE=4, find the length of DF. **Chart/Diagram Description:** * **Type:** Geometric figure (rectangle with internal lines and angles). * **Main Elements:** * **Shape:** Rectangle ABCD. * **Points:** Vertices A, B, C, D of the rectangle. Point E is on the side BC. Point F is on the line segment AE. * **Lines:** Sides of the rectangle AB, BC, CD, DA. Diagonal-like line segment AE. Line segment DF. * **Angles:** * Right angles at the vertices of the rectangle: ∠B, ∠C, ∠D, ∠A (implied). * Right angle at F, indicated by a square symbol: ∠DFA = 90° (since DF⊥AE). * Right angle at B: ∠ABE = 90° (since it's a corner of the rectangle). * **Labels:** Points are labeled A, B, C, D, E, F. The right angle at F is labeled with a square symbol. The right angle at B is implied by the rectangle. * **Relative Position:** A is top-left, B is bottom-left, C is bottom-right, D is top-right. E is on the bottom side BC, between B and C. F is on the line segment AE, and DF is perpendicular to AE.