The hourglass theorem of triangle

For example, the hourglass principle means that the hourglass theorem is the eight-character theorem, which consists of two similar triangles △ABC and△ △XYZ, with areas of S 1 and S2, respectively, and S 1: S2 = AB BC: XY YZ. The hourglass theorem and butterfly theorem are mostly used to divide the diagonal of a trapezoid into four triangles. The hourglass theorem can usually calculate the area ratio of the upper triangle and the lower triangle, and the butterfly theorem can calculate the area ratio of the four triangles.