“直角三角形斜边上的中线等于斜边的一半”,这条定理反映了直角三角形中重要的数量特征.在某些几何证题中,如能巧妙地运用这一数量关系,常可寻求到解题的捷径.下面举例说明. 例1 如图1,已知△ABC中,BD、CE分别是AC和AB边上的高.F、G分别是BC和DE的中点.求证:FG⊥ED. “The median line on the hypotenuse of a right-angled triangle is equal to half the hypotenuse,” and this theorem reflects the important quantitative characteristics of right-angled triangles. In some geometrical proofs, if one can skillfully use this quantitative relationship, one can often seek to The shortest way to solve problems is illustrated below. Example 1 As shown in Figure 1, in △ABC, BD and CE are the heights on the AC and AB sides, respectively. F and G are the midpoints of BC and DE, respectively. Proof: FG⊥ ED.