 Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.  Plane Geometry - Page 131by Arthur Schultze - 1901Full view - About this book
 | Harvard University - Geometry - 1899 - 39 pages
...If two triangles have their sides respectively proportional, the triangles are similar. THEOREM V. The bisector of an angle of a triangle divides the opposite side into segments proportional to the sides of the angle. THEOREM VI. 10 Conversely, if two polygons are similar, they... | |
 | United States Naval Academy - 1899 - 624 pages
...internally at C and externally at D ; which are the internal segments'? and which the external? Prove that the bisector of an angle of a triangle divides the opposite side internally and externally into segments proportional to the adjacent sides. (e) The sides of a triangle... | |
 | Arkansas. State Department of Public Instruction - Education - 1900 - 236 pages
...To describe upon a given straight line a segment of a circle which shall contain a given angle. 9. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. 10. Upon a given line to construct a polygon similar... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...552. Demonstrate that there is omy one point that divides a given .line internally in a given ratio. PROPOSITION XVII. THEOREM 287. The bisector of an...sides. AD c Hyp. In A ABC, BD bisects Z ABC. To prove AB :BC = AD: DC. Proof. Draw AE II DB, to meet CB produced in E. ZE = Z CBD. (89) Z CBD = Z ABD. (Hyp.)... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...coincide. CE. Ex. 551. In the diagram for Prop. XVI, if AB=12, BC = 16, AD = 15, DE = 20, is.BD\'CE? in E'. PROPOSITION XVII. THEOREM 287. The bisector of an...sides. AD c Hyp. In A ABC, BD bisects Z ABC. To prove AB : BC = AD : DC. Proof. . Draw AE II DB, to meet CB produced in E. ZE = Z CBD. (89) Z CBD = Z ABD.... | |
 | Arthur Schultze - 1901 - 392 pages
...BD II CE. aE.D. Ex. 551. In the diagram for Prop. XVI, if AB =12, BC = 16, AD= 15, DE = 20, \nBDlCE? PROPOSITION XVII. THEOREM 287. The bisector of an...segments having the same ratio as the other two sides. «- — ^_ A 7> 0 Hyp. In A ^5(7, BD bisects Z ABC. To prove AB:BC = AD: DC. Proof. Draw -4.E II DB,... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...side of a triangle divides the other two sides in the same ratio, and conversely. §§ 242, 244. (2) The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. § 245. (3) If two similar polygons are divided into triangles... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...triangle form a second triangle that is similar to the given triangle. PROPOSITION XIX. THEOREM. 502. The bisector of an angle of a triangle divides the opposite side into segments that are proportional to the adjacent sides of the angle. A"" D Let BD be the bisector of Z R of the... | |
 | George Albert Wentworth - Plane trigonometry - 1902 - 286 pages
...p. 64, become when one of the angles is a right angle ? 2. Prove by means of the Law of Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides. 3. What does Formula [26] become when A = 90° ? when A =... | |
 | Theophilus Nelson - Geometry, Modern - 1902 - 154 pages
...proportional to the other two sides ? What may be inferred from this in regard to the manner in which the bisector of an angle of a triangle divides the opposite side? Statement : — 216. A line may be divided internally or externally. A line is divided internally when... | |
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