Butterfly model, also known as trapezoid butterfly theorem, refers to four triangles connected by diagonal lines in a trapezoid. Trapezoidal butterfly theorem is an important theorem in plane geometry. Because the geometry of the theorem is peculiar and looks like a butterfly, it is named after the butterfly.

Proof of Trapezoidal Butterfly Theorem;

S 1 is similar to the triangle of S2, so the square of area ratio = side length ratio is a? ﹍b？ .

S 1 and S4 have the same base height, so we can know that S 1￣S4 = OA￣OC. Since s 1 and S2 are similar triangles, the similarity ratio is ￣ A ￣ B, so S1򠂓. ab； Similarly, s1\ uss3 = a? Ab company. So S 1︰S2︰S3︰S4=a? ﹍b？ ab； ab .