Beman, Wooster Woodruff, 1850-1922, Smith, David Eugene, 1860-1944 · Boston, Ginn & company · leaf 193
n 176 PLANE GEOMETRY. [Bk. IV. Proposition XIIL 249. Theorem. If any angle of a triangle is bisected, in-ternally or externally, by a line cutting the opposite side,then the opposite side is divided, internally or externally,respectively, in the ratio of the other sides of the triangle. … Given A ABC, the bisector of Z C meeting AB at P.To prove that AP : PB = AC : BC. Proof. 1. Let BE II PC, meeting AC produced at E, in Fig. 1.Then Z EBC = Z PCB = Z ACP = Z CEB. Given ; I. prop. XVII, cor. 2 2. ..BC=CE. Why? 3. But in A A BE, AP : PB = A C: CE, Prop. X, cor. 1and .. AP : PB = AC:…
Geometry
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