一平移梯形的腰过梯形上底上的一点作腰的平行线,将梯形问题变成平行四边形及三角形问题来解决.例1如图1,梯形ABCD中,AD∥BC,E、F分别为AD、BC的中点,∠B+∠C=90°,求证:EF=1/2(BC-AD).解析:由于BC-AD是两底的差,于是想到“平移两腰”.如图2,过E点分别作EM∥AB,EN∥DC,交BC于M、N,得(?)ABME、(?)DCNE和Rt△AMNE,则MN=BC-AD.因∠B+∠C=90°,则∠1+∠2=90°,∠MEN=90°.因F是MN的中点,故EF=1/2MN,则 A translating trapezoidal waist through the trapezoid on the bottom of a point for the waist of the parallel lines, the trapezoidal problem into parallelogram and triangle problem to solve.Example 1 Figure 1, trapezoidal ABCD, AD∥BC, E, F were AD, the midpoint of BC, ∠B + ∠C = 90 °, verify: EF = 1/2 (BC-AD) Analysis: Because BC-AD is the difference between the two ends, so think “translate two waist ”. As shown in Fig. 2, EM = AB, EN //DC, and BC / M, N, ABME, (?) DCNE and Rt △ AMNE, respectively, C = 90 °, then ∠1 + ∠2 = 90 °, ∠MEN = 90 °. Since F is the midpoint of MN, EF = 1 / 2MN, then