三角形问题---**47. 【问题回顾】** 我们知道 有两个角相等的三角形是等腰三角形 (简称“等角对等边”)． 其证明方法：如图 1，在△ABC中，∠B＝∠C，作顶角∠BAC的平分线AD，交BC边于点D，利用“AAS”可以证明△ABD≌△ACD，可得AB＝AC．其本质是利用了图形的轴对称性． **图 1 描述:** * Type: Geometric figure (Triangle). * Main Elements: * Points: A, B, C, D. * Lines: Line segments AB, AC, BC, AD. * Shape: Triangle ABC. Point D is on line segment BC. * Labels: Points are labeled A, B, C, D. The figure is labeled "图 1". * Relative Position: A is the top vertex. BC is the base. D is a point on BC, between B and C. AD connects A to D. **【类比探究】** 某数学兴趣小组在三角形“等角对等边”定理的基础上，提出猜想：在三角形中，大的内角所对的边也大，即“大角对大边”．转化为数学符号语言为： (1)已知：在△ABC中，∠ACB > ∠B．求证：AB > AC． 数学兴趣小组学生发现，该命题也可利用轴对称证明：作BC的垂直平分线，交AB于点D，交BC于点E，连接DC (如图 2)，请你帮助数学兴趣小组完成证明． **图 2 描述:** * Type: Geometric figure (Triangle). * Main Elements: * Points: A, B, C, D, E. * Lines: Line segments AB, AC, BC, DE, CD (dashed). * Shape: Triangle ABC. * Labels: Points are labeled A, B, C, D, E. The figure is labeled "图 2". Tick marks on BD and CD suggest BD=CD. A small square symbol at E on BC and the dashed line DE suggests DE is perpendicular to BC. * Relative Position: D is on AB. E is on BC. DE is drawn from D to E. CD is drawn from C to D as a dashed line. DE appears to be the perpendicular bisector of BC, suggesting E is the midpoint of BC and DE is perpendicular to BC. D is on AB. **【知识应用】** 请利用在三角形中，大的内角所对的边也大，即“大角对大边”这一结论完成下列问题： (2)已知，△ABC中，AC＝3，BC＝5，且∠C > ∠A > ∠B，则AB边的取值范围为______． (3)已知，如图 3，在△ABC中，AD平分∠BAC，点E为AC边上任意一点(不与点A，点C重合)，连接BE交AD于点F．求证：BF > FE． **图 3 描述:** * Type: Geometric figure (Triangle). * Main Elements: * Points: A, B, C, D, E, F. * Lines: Line segments AB, AC, BC, AD, BE, BF, FE. * Shape: Triangle ABC. * Labels: Points are labeled A, B, C, D, E, F. The figure is labeled "图 3". * Relative Position: D is on BC. AD connects A to D. E is on AC. BE connects B to E, intersecting AD at F. * Angles: Arcs at angle BAC divided by AD suggest AD is the angle bisector of ∠BAC.