PROPOSITION XIII 202. Theorem. The bisector of an exterior angle of a triangle divides the opposite side externally into segments proportional to the adjacent sides. 203. Sch. If a line is divided so that the ratio between its internal segments equals the ratio between its external segments, the line is said to be divided harmonically. The bisector of an angle of a triangle and the bisector of the exterior angle at the same vertex divide the opposite side of the triangle harmonically, because the ratios between the segments of this side, both internal and external, equal the ratio between the adjacent sides. SIMILAR POLYGONS 204. Definition. Two polygons are similar when they are mutually equiangular and have their homologous sides proportional. B M and N (Fig. 3) are not similar, even if the homologous between homologous sides is the ratio of similitude of the figures. |