 The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.  Plane and Solid Geometry - Page 162by George Albert Wentworth, David Eugene Smith - 1913 - 470 pagesFull view - About this book
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...bisector compare with the ratio of the sides of the triangle adjacent to these segments ? Theorem. The bisector of an angle of a triangle divides the...segments which are proportional to the adjacent sides. Data: Any triangle, as ABC, and CD the bisector of one of its angles, ACB. To prove AD : DB = AC :... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...such that M'A:M * B = 3:5. (2) Comparing (1) and (2), MA: MB = M'A: M'B. PROPOSITION XV. THEOREM. 348. The bisector of an angle of a triangle divides the...segments which are proportional to the adjacent sides. E AMB Let CM bisect the angle C of the triangle CAB. To prove that MA : MB = CA : CB. Proof. Draw AE... | |
 | William James Milne - Geometry - 1899 - 404 pages
...bisector compare with the ratio of the sides of the triangle adjacent to these segments ? Theorem. The bisector of an- angle of a triangle divides the...segments which are proportional to the adjacent sides. A Data: Any triangle, as ABC, and CD the bisector of one of its angles, ACB. To prove AD : DB = AC... | |
 | 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...segments which are proportional to the adjacent sides. 10. Upon a given line to construct a polygon similar to a given polygon. 1. Factor: ALGEBRA. (1) lay... | |
 | Charles Hamilton Ashton - Geometry, Analytic - 1900 - 292 pages
...the angle F'P^. It is a well-known theorem of elementary geometry that the bisector of an interior angle of a triangle divides the opposite side into...segments which are proportional to the adjacent sides of the triangle. The converse theorem is also true. It is therefore sufficient to show that pip F,N... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...ABE is a mean proportional between ADE and ABC. PROPOSITION XVIII. — THEOREM. The bisector of any angle of a triangle divides the opposite side into segments which are proportional to the other two sides. Given. — Let the line AD bi- .js sect the angle A of the triangle ,.••' :' ABC.... | |
 | 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...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 angle of a triangle divides the opposite side into segments having the same ratio as the other two sides. AD c Hyp. In A ABC, BD bisects Z ABC. To prove AB : BC... | |
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