 | Theophilus Nelson - Geometry, Modern - 1902 - 154 pages
...proportional to the other two sides ? What may be inferred from this in regard to the manner in which the bisector of an angle of a triangle divides the opposite side? Statement : — 216. A line may be divided internally or externally. A line is divided internally when... | |
 | 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...are proportional to the adjacent sides of the angle. Let BD be the bisector of ZB of the A ABC. „, -, AD AB To Prove -= DC JSC Proof. Prolong AB until... | |
 | 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 opposite side into segments proportional to the adjacent sides. 169. Theorem IX. If two polygons are composed of the same number... | |
 | 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... | |
 | George Albert Wentworth, George Anthony Hill - Logarithms - 1903 - 348 pages
...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... | |
 | 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... | |
 | Alexander Ziwet - Mechanics - 1904 - 513 pages
...is the velocity of -4. (6) ^= 28.3, VM— 22.4 ft./sec. Page 140. (3) Based on the proposition that the bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. (5) The center of the incircle of the triangle formed by the midpoints... | |
 | 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... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...P and P'. PROOF. PA : PB = 2 : 5, Const, and P'A : 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. D HYPOTHESIS. In the A ABC, AD bisects the ^ A. CONCLUSION.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...B~ C .-.AX=AE(1) (300). .-. DX and DE coincide (?) (39). That is, DE is II to BC. QED 308. THEOREM. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the other two sides. Given : A ABC ; BS the bi- p;>.. : x ~-... sector of... | |
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Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides. 
