三角形中位线定理和梯形中位残定理分别揭示了三角形的中位线与第三边及梯形的中位线与上、下底之间的位置关系和数量关系．应用这两个定理既可以判定两线段的平行关系又可以确定线段之间的信半关系与和差关系．它们在几何证题中有着举足轻重的作用．现举例说明，供参考．例1如 The triangle median line theorem and the trapezoidal middle position theorem respectively reveal the positional relationship and the quantitative relationship between the median line of the triangle and the third edge, the trapezoidal median line, and the upper and lower bases. The application of these two theorems can not only determine the parallel relationship between two line segments, but also determine the relationship between the line segment and the relationship between the two. They play a decisive role in geometrical proofs. Here is an example for reference. Example 1