尝试解这道题目---**Problem Description:** 如图, 已知△ABC是等腰直角三角形, AB = AC, AD是斜边的中线, E、F分别是AB、AC边上的点, 且DE⊥DF, 若BE=8, CF=6. **Questions:** (1)求证: △AED≌△CFD; (2)求△DEF的面积. **Diagram Description:** * **Type:** Geometric figure. * **Main Elements:** * A triangle ABC is shown. * Point D is on the side BC. Line segment AD is drawn from A to D. * Point E is on the side AB. Line segment DE is drawn. * Point F is on the side AC. Line segment DF is drawn. * Line segment EF is drawn. * **Labels:** Vertices A, B, C and points D, E, F are labeled. * **Relationships and Properties (based on text and diagram):** * △ABC is an isosceles right triangle with AB = AC. The right angle is at A (implied by standard convention for isosceles right triangle notation). * AD is the median to the hypotenuse BC, meaning D is the midpoint of BC. * E is on AB and F is on AC. * DE is perpendicular to DF (∠EDF = 90°).