近年来的中考中,与等腰梯形有关的探索题屡见不鲜,下面解析两例.例1如图1,等腰梯形ABCD中,AD∥BC,M、N分别是AD,BC的中点,E、F分别是BM、CM的中点.(1)求证:四边形MENF是菱形.(2)若四边形MENF是正方形,请探索等腰梯形ABCD的高和低边BC的数量关系并说明理由.(2005年广东省中考题) In recent years, during the middle school exams, exploration questions related to isosceles trapezoids are commonplace. Two examples are illustrated below. Example 1 In Figure 1, isosceles trapezoid ABCD, AD∥BC, M, and N are the midpoints of AD and BC, respectively. F and F are the midpoints of BM and CM, respectively. (1) Verify that the quadrilateral MENF is a rhombus. (2) If the quadrilateral MENF is a square, explore the relationship between the high and low sides of the isosceles trapezoid ABCD and explain why. 2005 Guangdong Provincial Examination Questions)