关于中线互相垂直的三角形 ,有一个十分有趣的性质 ,我们归结如下 :定理　如果三角形中两中线互相垂直 ,那么两中点所在边的平方和等于第三边平方的 5倍 ,反之亦然 .证明　如图 1,△ＡＢＣ中 ,中线ＢＤ、ＣＥ互相垂直于Ｆ ,显然Ｆ为△ＡＢＣ的垂心 ,则ＢＦ =23 ＢＤ ,ＣＦ =23 The triangles that are perpendicular to each other on the center line have a very interesting property. We sum it up as follows: Theorem If the two center lines in a triangle are perpendicular to each other, then the sum of squares of the sides where the two midpoints are is equal to 5 times the square of the third side, and vice versa. In Figure 1, in △ABC, the midline BD and CE are perpendicular to F, obviously F is the vertigo of △ABC, then BF =23 BD, CF =23