...Oy such that Oy : xy is the same for every such point y. MEASUREMENT OF LINE-SEGMENTS. 250. THEOREM. The bisector of an angle of a triangle divides the opposite side into segments whose ratio is the same as that of the adjacent sides. Given CD bisecting ZC in A ABC. To prove that...

...compute the third side BC. Ex. 1122. Divide the circumference of a circle into three parta that shall be in the ratio of 1 to 2 to 3. Ex. 1123. The circles...vertices of the hexagon ; (c) the area of the ring bounded by the circumference of the given circle and that of the circle inscribed in the hexagon. Ex....

...the product of the two segments of one is equal to the product of the two segments of the other. 5. Prove that the bisector of an angle of a triangle divides the opposite side into segments which are proportional to the other two sides. The bisectors of the angles B, C meet the opposite sides...

...triangle divided by the sine of the angle opposite that side. 2. By means of the property of sines, prove that the bisector of an angle of a triangle divides the opposite side into segments which are proportional to the sides forming the given angle. 3. In any triangle ABC, prove that a =...

...the base or above the vertex, and also in which the parallel is drawn through the vertex. THEOREM. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. The proposition relating to the bisector of an exterior...

...192 .-. EA = EB. Ax. 8 Similarly, it may be shown that FC = FD. QED 4. If a line drawn from a vertex of a triangle divides the opposite side into segments proportional to the adjacent sides, the line bisects the angle at the vertex. Given, in A-4BC, line CM drawn, cutting AB in M so that AM:MB...

...equal to the square of the tangent from P to C if P is an external point. [Ni8.] 3. The bisector of any angle of a triangle divides the opposite side into segments proportional to the adjacent sides. [Half of N6.] 4. To construct a triangle similar to a given triangle. [*] (Drawing triangles to scale;...

...equal to the square of the tangent from P to C if P is an external point. [N18.] 3. The bisector of any angle of a triangle divides the opposite side into segments proportional to the adjacent sides. [Half of N6.] 4. To construct a triangle similar to a given triangle. [*] (Drawing triangles to scale;...

...side is to its corresponding segment, then t/te line is parallel to the third side. 149. Theorem III. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the sides of the angle. 150. Theorem IV. If a series of parallels be cut...

...segments having the same ratio, the line is said to be divided harmonically. PROPOSITIOK XI. THEOREM 279. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. M Given the bisector of the angle C of the triangle ABC,...