 | Matilda Auerbach, Charles Burton Walsh - Geometry, Plane - 1920 - 408 pages
...harmonically? Discuss Theorems 31 and 32 from the point of view of external division of a sect. Theorem 32<z. The bisector of an angle of a triangle divides the opposite side into sects which are proportional to the adjacent sides. Given: AABC; D on AB and %.ACD = %.DCB. AD AC To... | |
 | Marquis Joseph Newell - 1920 - 424 pages
...the hypotenuse, the perpendicular is a mean proportional between the segments of the hypotenuse. V. The bisector of an angle of a triangle divides the opposite side into segments that are proportional to the adjacent sides of the angle. VI. If, from a point without a circle,... | |
 | William Fogg Osgood, William Caspar Graustein - Geometry, Analytic - 1921 - 650 pages
...between the focal radii. To prove this proposition we recall the theorem of Plane Geometry which says that the bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. It is easily seen that the converse * of this... | |
 | Robert Remington Goff - 1922 - 136 pages
...: Divide a given straight line into parts proportional to any number of given straight lines. *24Q. The bisector of an angle of a triangle divides the opposite side into parts proportional to the other two sides. *251. The bisector of an exterior angle of a triangle divides the opposite side, externally,... | |
 | Clarence Addison Willis - Geometry, Modern - 1922 - 320 pages
...each to each, to two angles of another triangle, the triangles are similar. Why? 245. Theorem V. — The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. State the hypothesis and the conclusion. Helps. — (1)... | |
 | Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...direction of AB as positive and the direction of BA as negative, then AP + PB — AB. 359. Theorem. The bisector of an angle of a triangle divides the opposite side internally into segments proportional to the adjacent sides. D FIG. 358 B Given the triangle ABC, with... | |
 | Clarence Addison Willis - Geometry, Modern - 1922 - 318 pages
...each to each, to two angles of another triangle, the triangles are similar. Why? 245. Theorem V.—The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. State the hypothesis and the conclusion. Helps. — (1)... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...external segment is equal to the product of the other secant and its external segment. THEOREM 106. The bisector of an angle of a triangle divides the opposite side internally into segments that have the same ratio as the other two sides of the triangle. THEOREM 107.... | |
 | David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...the A are given similar. §205 BOOK in Proposition 12. Bisector of an Interior Angle 227. Theorem. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. Given the bisector of ZC of the AABC, meeting... | |
 | David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...third side. 7. Three or more parallel lines cut off proportional segments on any two transversals. 8. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. 9. If the bisector of an exterior angle of a... | |
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The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 
