长方体的对角线有如下性质:长方体一条对角线的平方等于一个顶点上三条棱的平方和.即对角线长为 l=(a~2+b~2+c~2)~(1/2)(a、b、c 为长方体长、宽、高)(立体几何课本 P_(54))证明略.推论1 长方体的对角线相等且三组相对的矩形的对角线分别相等.推论2 长方体对角线与共顶点的三个 The diagonal of a cuboid has the following properties: The square of a diagonal of a cuboid is equal to the sum of the squares of the three edges of a vertex. That is, the length of the diagonal is l=(a~2+b~2+c~2)~(1). /2) (a, b, and c are cuboid length, width, and height) (stereo-textured textbook P_(54)) proves slightly. Corollary 1 The diagonals of the cuboids are equal and the diagonals of the three sets of opposing rectangles are equal. Inference 2 of the cuboid diagonal and the common vertices