为了拓广几何的解题途径。我们对平面中有关三条直线共点而又被另一些直线相截这类问题进行了精浅的研究,由三角形的面积公式出发推得一个较有实用价值的几何定理。因为它揭示了三条共点射线被另外直线截割而产生的张角正弦值与截得线段之间的比例关系。为叙述方便起见,权且将它定名为“截割角边比定理”(是否妥当,尚需商榷)。运用截割角边比定理来证明几何中的有关截交一类的定理(如梅涅劳斯定理,蝴蝶定理等)以及线段相等,不等与成比例等问题,具有思路明朗,书写简捷,规律性强等点。因此,这一定理值得重视。一截割角边比定理共点三射线PM,PN,PK被直线EF相截,其交点分别为A,B,C(如图所示),设∠APC=a,∠BPC=β,则 In order to broaden the solution to the problem of geometry. We have done a superficial study on the problem of three points in the plane that are common to each other and intersected by some other straight lines. A geometrical theorem is derived from the area formula of the triangle. This is because it reveals the proportional relationship between the sine angle of the splay angle and the intercepted line segment resulting from the cutting of three common ray rays by another straight line. For the sake of narrative convenience, the right name is “the cut edge angle ratio theorem” (whether it is appropriate or not). The use of the cut-angle-edge-ratio theorem to prove the theorem about the type of interception in geometry (such as Menelaus theorem, butterfly theorem, etc.) and the problem of equal, unequal and proportional segments, with clear thinking and simple writing Regularity is strong. Therefore, this theorem deserves attention. A cutting angle-side ratio theorem co-points three-ray PM, PN, and PK to be intercepted by a straight line EF. Its intersections are A, B, and C (as shown in the figure). Let ∠APC=a and ∠BPC=β.