| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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°... | |
| 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."... | |
| 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... | |
| 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... | |
| 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,... | |
| 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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