习题大多是经过精挑细选,可作为“定理”使用的经典题,做习题时,除全方位寻求多种解法外,还要拓展其潜在的价值,以沟通数学知识间的联系,不断完善自己的知识结构,从学会走向会学. 人教版《几何》有这样一道习题:如图1,梯形ABCD中,点E、F分别在腰AB、CD上,EF∥AD,AE:EB=m:n,求证:(m+n)EF=mBC+nAD.你能由此推出梯形的中位线公式吗? 很明显,此题是梯形中位线定理的推广形式.若能以此题为模式进行研究,则既可丰 Most of the exercises are carefully selected and can be used as classic themes for the theorem. When doing exercises, in addition to seeking a variety of solutions in all directions, they must also expand their potential value to communicate the relationship between mathematical knowledge. Constantly improve their knowledge structure, from learning to learning. PEP “geometry” has such an exercise: Figure 1, the trapezoid ABCD, points E, F on the waist AB, CD, EF AD, AE: EB=m:n, verify: (m+n)EF=mBC+nAD. Can you derive the trapezoid median line formula? Obviously, this is the generalized form of the trapezoid median line theorem. This title is a model for research, then both