...proportion ; AB AD ."."., which gives, =-— = =— ; that is — A straight line mliO JJU secting an angle of a triangle, divides the opposite side into parts proportional to the adjacent sides. 103. Let us now take an obtuse-angled triangle, as Fig. 49. ABC (fig, 49) and draw perpendiculars from...

...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...

...equation (3), which gives, when m = n, that is, AD = \AB, which was to be proved. 3. Any angle-bisector of a triangle divides the opposite side into parts proportional to the adjacent sides. When CD bisects C, we have found, (Eq. (3) ), „7 AD=y = .: DB=ly = m +n ml m + n Dividing, we have...

...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,...

...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...

...should be written b-а tea. \ (В -А) + a tan i (В + A) EXERCISE XII. 1. What do the formulas of § 36 become when one of the angles is a right angle ? 2....of a triangle divides the opposite side into parts pro> portional to the adjacent sides. 3. What does Formula [26] become when A = 90° ? when A = 0°...

...the right bisector of the join of the given points. The proof is clear by citing the familiar theorem that the bisector of an angle of a triangle divides the opposite side in the ratio of the including sides. PHYSICS. Answer any eight. 1. Explain the "parallelogram of forces."...

...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 whi^h are proportional to the adjacent sides. 3. The area of a parallelogram is equal to the...

...142. Theorem. Lines meeting in a common point divide parallels into proportional parts. 143. Theorem. 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...

...radii of their circumscribed circles.) But, since OF bisects the £ COE, .: OC : OE : : CF : FE, (523. The bisector of an angle of a triangle divides the opposite side in the ratio of the other two sides of the triangle.) .'. q : p : : CF : FE, whence, by composition,...