 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 divides the opposite side produced into segments proportional to the other...  Plane and Solid Geometry: Teacher's Edition - Page 192by George Albert Wentworth, George Wentworth - 1912 - 590 pagesFull view - About this book
 | Euclides - 1821 - 294 pages
...always as expressed in the above demonstration. PROP. III. THEOR. A right line bisecting any angle of a triangle, divides the opposite side into segments proportional to the other two sides. And tf a right line drawn from any angle of a triangle, divide the opposite side into... | |
 | Euclides - 1865 - 402 pages
...proportionally, it is parallel to the remaining side . . . . . 2. A straight line bisecting the angle of a triangle divides the, opposite side into segments proportional to the conterminous sides ; I And conversely, if a straight line drawn from any angle of a j- VI. 3. triangle... | |
 | United States Naval Academy - 1874 - 888 pages
...intersecting without the circumference' ? Prove the latter. 3. Prove that the line which bisects either angle of a triangle divides the opposite side into segments proportional to the adjacent sides. The hypothenuse of a right triangle is a and one of the adjacent ;in<;li's is 30e, a line is drawn bisecting... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...good where there is any number of radiating lines. PROPOSITION XIV. THEOREM. The Msectrix of any angle of a triangle divides the opposite side into segments proportional to the adjacent sides. Let DK bisect the angle CDA of the triangle ACD ; then AK : KG :: AD : CD. Prolong CD till DE is equal... | |
 | Edward Olney - Geometry - 1876 - 354 pages
...BISECTOR OF AN ANGLE OF A TRIANGLE. PROPOSITION IV. 358. Theorem.—A line which bisects any angle of a triangle divides the opposite side into segments proportional to the adjacetit sides. DEM.—Let CD bisect the angle ACB; then AD : DB :: AC : CB. For, draw BE parallel... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...the triangles ABC and DEF are equiangular; PROPOSITION XI.—THEOREM. A line which bisects any angle of a triangle, divides the opposite side into segments proportional to the other two sides. Let the line DB bisect the angle ABC of the given triangle ACB; then will the segments... | |
 | Education - 1928 - 684 pages
...similarity of polygons. 4. The sum of the exterior angles of a polygon. 5. The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 6. The bisector of an exterior angle of a triangle divides the opposite side externally into segments... | |
 | Arthur Sherburne Hardy - Quaternions - 1881 - 248 pages
...diagonal of a parallelogram is an angle-bisector, the parallelogram is a rhombus. 6. Any angle-bisector of a triangle divides the opposite side into segments proportional to the other two sides. 7. The line joining the middle point of the side of апз' parallelogram with oiie... | |
 | Edward Olney - Geometry - 1882 - 262 pages
...BISECTOR OF AN ANGLE OF A TRIANGLE. PROPOSITION IV. 358. Theorem. — A line which bisects any angle of a triangle divides the opposite side into segments proportional to the adjacent sides. DEM.— Lei CD bisect the angle ACB; then AD : DB : : AC : CB. For, draw BE parallel to CD, and produce... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...BISECTOR OF AN ANGLE OF A TRIANGLE. PROPOSITION IV. 405. Theorem.—A line which bisects any angle of a triangle divides the opposite side into segments proportional to the adjacent sides. Draw BE parallel to CD, and produce it till it meets AC produced in E. By reason of the parallels CD... | |
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