...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 segments proportional...

...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...

...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,...

...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...

...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...

...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...

...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 AD and DC be...

...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 opposite side into segments proportional to the adjacent sides. 6. The bisector of an exterior angle of a triangle divides the opposite side externally...

...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,...

...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 of its opposite...