 Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.  Complete School Algebra - Page 466by Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1919 - 507 pagesFull view - About this book
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...of Prop. 84. DE and AF should both be taken equal to the second line. Proposition 86. Theorem. 118. The bisector of an angle of a triangle divides the...segments which are proportional to the adjacent sides. BDC Hypothesis. In the A ABC, AD is the bisector of the ZCAB. Conclusion. BD : DC : : AB : AC. Proof.... | |
 | George Albert Wentworth - Geometry - 1899 - 500 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. AM B Let CM bisect the angle C of the triangle CAB. To prove that MA : MB = CA : CB. Proof. Draw AE... | |
 | 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 :... | |
 | 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 - 294 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.... | |
 | 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...omy one point that divides a given .line internally in a given ratio. 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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