 | Euclides - 1821 - 294 pages
...they are 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
...produced, 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... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...holds 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... | |
 | 1876 - 646 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 which are proportional to the adjacent sides. 3. The area of a parallelogram is equal to the product... | |
 | Edward Olney - Geometry - 1876 - 354 pages
...OF THE 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
...and 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
...similar polygons. 3. Test for similarity of polygons. 4. The sum of the exterior angles of a polygon. 5. The bisector of an angle of a triangle divides the...into segments proportional to the adjacent sides. 6. The bisector of an exterior angle of a triangle divides the opposite side externally into segments... | |
 | George Anthony Hill - Geometry - 1880 - 348 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,... | |
 | 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... | |
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... that the bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 
