 | George Bruce Halsted - Geometry - 1886 - 394 pages
...radii of their circumscribed circles.) But, since OF bisects the 4 COE, .: OC : OE :: CF : FE, (523. The bisector of an angle of a triangle divides the opposite side in the ratio of the other two sides of the triangle.) .-. q : p : : CF : FE, whence, by composition,... | |
 | George Albert Wentworth - Trigonometry - 1887 - 200 pages
...cos A = l. ac csin A sin С When A = 180°, cos .a = - 1. ••*-»+* + »» D •П J •*.* /Hf 2. Prove by means of the Law of Sines that the bisector...side into parts proportional to the adjacent sides. 6 = Л.(7. a = 6 - c. R -^ /Tf a = -BC". e = B A. 6 = Л(7. a = 6 + c. Let CD bisect angle C. Then... | |
 | George Albert Wentworth - Trigonometry - 1888 - 186 pages
...quantities, the formula in this case should be written 6 - a _ tan } ( В - A) b + a - tan } (B + A) EXERCISE XII. 1. What do the formulas of § 36 become when...of a triangle divides the opposite side into parts pro^ portional to the adjacent sides. 3. What does Formula [26] become when A = 90° ? when A = 0°1... | |
 | George Albert Wentworth - Surveying - 1889 - 360 pages
...formulas of § 36 become when one of the angles is a right angle ? 2. Prove by means of the Law 01 Sines that the bisector of an angle of a triangle divides the opposite side into parts pro> portional to the adjacent sides. 3. What does Formula [26] become when A = 90° ? when A = 0°... | |
 | George Albert Wentworth - 1889 - 276 pages
...142. Theorem. Lines meeting in a common point divide parallels into proportional parts. 143. Theorem. The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 144. Theorem. The bisector of an exterior angle of a triangle... | |
 | George Albert Wentworth - 1889 - 264 pages
...142. Theorem. Lines meeting in a common point divide parallels into proportional parts. 143. Theorem. The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 144. Theorem. The bisector of an exterior angle of a triangle... | |
 | De Volson Wood - Geometry, Analytic - 1890 - 372 pages
...equation (3), which gives, when m = n, that is, AD — ^AB, which was to be proved. 3. Any angle-bisector of a triangle divides the opposite side into parts proportional to the adjacent sides. When CD bisects C, we have found, (Eq. (3)), nl .-. DB=ly = TO +71 ' ml TO + n Dividing, we have AD__riL_... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...difference of two external segments. BOOK III.— PROPORTIONAL LINES. Proposition 14. Theorem. 303. The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. Hyp. Let AD bisect the ZA of the A ABC. To prove DB :... | |
 | Euclid - Geometry - 1890 - 442 pages
...forming the angle, so as to be terminated by these lines, the parallels so drawn are equal. 13. If the bisector of an angle of a triangle divides the opposite side unequally, the greater segment is adjacent to the greater side. 14. If an altitude of a triangle divides... | |
 | George Albert Wentworth - 1891 - 206 pages
...Л = 0°, cos Л = 1. Ь sin B а c csin A sin C Ь c sin B sin C When Л = 180°, cos Л' 1. 1 BC 2. Prove by means of the Law of Sines that the bisector...angle of a triangle divides the opposite side into parte proportional to the adjacent sides. Ь = AC. а = b-е. B ^ C a = BC. c = BA. 6 = ЛС a = 6... | |
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The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 
