梯形中位线定理是指:梯形两腰中点的连线平行于两底,且等于两底和的一半。本文就梯形中位线定理的推广及其应用,作点讨论。一、推广我们先考虑在二维空间的推广。如果在梯形中,有一线段,不是梯形两腰中点的连线,而是两腰上定比分点的连线,则有定理1 梯形ABCD中,若直线PQ与腰AB、DC分别相交于P、Q,且AP:PB=DQ:QC=m:n,则PQ平行于两底,且PQ=mBC+nAD/(m+n)。证如图1,设两腰 The trapezoid median line theorem means that the line connecting the midpoints of the trapezoids is parallel to the two bases and is equal to half the sum of two bases. In this paper, the popularization and application of trapezoidal median line theorem are discussed. First, promotion We first consider the promotion of two-dimensional space. If there is a line segment in the trapezoid, it is not the line connecting the midpoints of the trapezoid and the two waists, but the line connecting the two waists at a certain point. There is Theorem 1. In the trapezoid ABCD, if the line PQ intersects with the waist AB and DC, respectively, Q, and AP: PB = DQ: QC = m: n, then PQ is parallel to both bases, and PQ = mBC + nAD/(m + n). Certificate shown in Figure 1, set two waist