 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...altitudes of similar triangles equals the ratio of similitude of the triangles. 168. Theorem VIII. The bisector of an angle of a triangle divides the...into segments proportional to the adjacent sides. 169. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each... | |
 | John Perry - Mathematics - 1903 - 142 pages
...drawn parallel to the base of a triangle divides the sides into proportionate segments. Prove that fhe bisector of an angle of a triangle divides the opposite side into segments proportional to the other side. In equiangular triangles the sides are in the same proportions. Divide a straight line... | |
 | Alan Sanders - Geometry - 1903 - 392 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. Let BD be the bisector of ZB of the A ABC.... | |
 | George Albert Wentworth, George Anthony Hill - Logarithms - 1903 - 348 pages
...XXXIV, p. 64, become when one of the angles is a right angle ? 2. Prove by means of the Law of Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides. 3. What does Formula [26] become when A = 90° ? when .4... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...triangle form by their intersection a triangle that is also equilateral. PROPOSITION XIX. THEOREM. 502. The bisector of an angle of a triangle divides the opposite side into .vegnicnts that are proportional to the adjacent sides of the angle. A- 5 Let BD be the bisector of... | |
 | Alexander Ziwet - Mechanics, Analytic - 1904 - 522 pages
...— c is the velocity of A . (6) z', = 28.3, vM=22.4 ft./sec. Page 140. (3^) Based on the proposition that the bisector of an angle of a triangle divides...into segments proportional to the adjacent sides. (5) The center of the incircle of the triangle formed by the midpoints of the sides. . (6) About 1000... | |
 | George Albert Wentworth - Geometry - 1904 - 496 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 opposite side into segments which are proportional to the adjacent sides. AM B Let CM bisect the angle C of the triangle CAB. To... | |
 | Education - 1904 - 350 pages
...between the whole secant and its external segment. Construct a mean proportional to two given lines. Prove that the bisector of an angle of a triangle divides the opposite sides into segments which are proportional to the adjacent sides. The base of a triangle is 6 feet,... | |
 | Education - 1911 - 946 pages
...equal to the square of the tangent from P to C if P is an external joint. [N18.] 3. The bisector of any angle of a triangle divides the opposite side into segments proportional to the adjacent sides. [Half of N6.] 4. To construct a triangle similar to a given triangle. [*] (Drawing triangles to scale;... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...harmonically at P and P'. PROOF. PA : PB = 2 : 5, Const, and PA: P'B = 2:5. Const. PROPOSITION XV. THEOREM 347 The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. HYPOTHESIS. In the A ABC, AD bisects the Z A. CONCLUSION.... | |
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... that the bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 
