以△ABC的三边为边, 在 BC 的同侧作三个正三角形, 即△ABD, △BEC, △ACF. 判断四边形 ADEF 的形状, 并证明你的结论.---**Extracted Content:** **Question 2:** 如图, 以△ABC的三边为边, 在 BC 的同侧作三个正三角形, 即△ABD, △BEC, △ACF. 判断四边形 ADEF 的形状, 并证明你的结论. **Relevant Text (Handwritten Solution Steps):** 解: △ABD, △BEC, △ACF 均为正三角形 ∴ BD=AB, BE=BC, AC=AF, ∠DBA = ∠EBC = ∠FCA = 60° ∴ ∠DBE = ∠ABC, ∠CBE = ∠CBA + ∠ABE ∠ABC = ∠DBA + ∠DBE ∠DBE = ∠ABC ∴ △DBE ≌ △ABC (SAS) ∴ DE = AC ∵ AC = AF ∴ DE = AF 同理可证 △EFC ≌ △ABC ∴ EF = AB ∵ AB = AD ∴ EF = AD ∴ 四边形 ADEF 是平行四边形. **Chart Description:** * **Type:** Geometric diagram. * **Main Elements:** * A triangle labeled ABC. * Three equilateral triangles built outwards on the sides of triangle ABC, all on the same side relative to BC (the top side in the diagram): * Triangle ABD is built on side AB. Angle at A is labeled 60°. Angle at B is labeled 60°. Vertex D is shown above/to the left of A and B. * Triangle BEC is built on side BC. Angle at B is labeled 60°. Angle at C is labeled 60°. Vertex E is shown above/to the right of B and C. * Triangle ACF is built on side AC. Angle at A is labeled 60°. Angle at C is labeled 60°. Vertex F is shown above/to the right of A and C. * A quadrilateral ADEF is formed by connecting vertices A, D, E, and F. Lines AD, DE, EF, and FA are drawn. * Right angle symbols are shown at vertices D and F, implying ∠AD E and ∠AFF are right angles. (Note: This might be an error in the drawing or a consequence derived from the problem/solution, but the symbol is present). Angles within the equilateral triangles are labeled 60°.