一、试题呈现题目:(2011年山东菏泽)如图1,在梯形ABCD中,AD∥BC,∠B=90°,∠C=45°,AD=1,BC=4,E为AB的中点,EF∥DC交BC于点F,求EF的长.该题是2011年山东省菏泽市的一道中考题,以直角梯形、直角三角形为素材,涉及平行线的性质、等腰直角三角形、三角形的全等和相似、梯形的中位线以及解直角三角形的相关知识,是一道难度 First, the test questions presented: (2011 Shandong Heze) Figure 1, in the trapezoidal ABCD, AD∥BC, ∠ B = 90 °, ∠ C = 45 °, AD = 1, BC = 4, E is AB Point, EF // DC to BC at point F, EF long. The title is a 2011 Shandong Province, Heze City, a test in the right trapezoid, right triangle as the material, involving the nature of parallel lines, isosceles right triangle, The congruence and similarity of the triangles, the median of the trapeziums, and the knowledge about the right triangles are a challenge