三角形的中位线定理揭示了其中位线与第三边的位置关系与数量关系,巧用它可以证明若干与线段中点有关的问题. 例1 如图1,△ABC中,BD 平分∠ABC,AD BD于D,E为AC的中点, 求证:DE∥BC. 证明:延长AD交BC于F. ∵BD平分∠ABC,又AD BD 于D,∴AD=FD,又∵AE= CE,由三角形中位线定理得: DE∥FC,∴DE∥BC. The triangle’s median line theorem reveals the positional relationship between the bit line and the third edge, and it can be used to demonstrate a number of problems related to the midpoint of the line segment. Example 1 As shown in Figure 1, in △ABC, the BD splits the ABC. , AD BD in D, E is the midpoint of AC, Proof: DE ∥ BC. Proof: to extend AD to pay BC in F. ∵ BD equally split ∠ ABC, AD BD in D, ∴ AD = FD, ∵ AE = CE , from the triangle median line theorem: DE∥FC, ∴DE∥BC.