Model features:
(1) Two parallel lines, the connecting lines of the endpoints intersect at the O point to form two triangles;
② The length ratio of two sides on the same straight line is equal to the length ratio of two parallel sides;
③ The area ratio of two triangles is equal to the square ratio of the length of two parallel sides.
We can remember the hourglass model and the butterfly model together. The two diagonal lines of the trapezoid intersect to form four triangles. The areas of the left and right triangles are equal (butterfly model), and the area ratio of the upper and lower triangles is equal to the square ratio of the two parallel sides of the trapezoid.
Hourglass model formula and butterfly theorem formula;
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.