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" The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. "
Plane Trigonometry - Page 53
by George Albert Wentworth - 1887
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 172 pages
...proportion ; AB AD ."."., which gives, =-— = =— ; that is — A straight line mliO JJU secting an angle of a triangle, divides the opposite side into parts proportional to the adjacent sides. 103. Let us now take an obtuse-angled triangle, as Fig. 49. ABC (fig, 49) and draw perpendiculars from...
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Report, Volumes 11-20

1876
...text-book you have studied and to what extent.] 1. To draw a common tangent to two given circles.' 2. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. 3. The area of a parallelogram is equal to the...
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The Elements of Coordinate Geometry: In Three Parts: 1. Cartesian Geometry ...

De Volson Wood - Geometry, Analytic - 1882 - 333 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) ), „7 AD=y = .: DB=ly = m +n ml m + n Dividing, we have...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 314 pages
...perpendicular let fall from the vertex of the right angle, (.) the length of this perpendicular. 10. Prove that the bisector of an angle of a triangle divides the opposite side into parts that have the same ratio as the adjacent sides. Hints. — If ABC is the triangle, BD the bisector,...
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Plane and Spherical Trigonometry

George Albert Wentworth - Trigonometry - 1882 - 201 pages
...the formula in this case should be written b - a _ tan i ( 5 - A) Ъ + a ~ tan I (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...
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Texas School Journal, Volume 20

Education - 1902
...the right bisector of the join of the given points. The proof is clear by citing the familiar theorem that the bisector of an angle of a triangle divides the opposite side in the ratio of the including sides. PHYSICS. Answer any eight. 1. Explain the "parallelogram of forces."...
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Wentworth & Hill's Exercise Manuals.(: Geometry

George Albert Wentworth - Geometry, Plane - 1884 - 228 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...
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Yale Examination Papers

F. B. Stevens - Examinations - 1884 - 175 pages
...text-book you have studied and to what extent.] 1. To draw a common tangent to two given circles. 2. The bisector of an angle of a triangle divides the opposite side into segments whi^h are proportional to the adjacent sides. 3. The area of a parallelogram is equal to the...
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...radii of their circumscribed circles.) But, since OF bisects the 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,...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 366 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,...
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