...part of this proposition, DE is parallel to DC. PROP. III. THEOR. — Tne straight line which bisects an angle of a triangle, divides the opposite side into segments which have the same ratio to one another as the adjacent sides of the triangle have : and (2) if the segments...

...of the homologous sides. PROPERTIES OF TRIANGLES FROM PROPORTIONAL LINES. 87. A line bisecting any angle of a triangle divides the opposite side into segments which are related to each other as the contiguous sides. Let AF (Fig. 75) bisect the angle A in the triangle...

...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 its base and altitude. 4....

...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...

...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,...

...angles, and their homologous sides are proportional (Euclid vi., Definition 1). 6. A line bisecting any angle of a triangle divides the opposite side into segments, which' are in the same ratio as the remaining sides of the figure (Euclid vi. 3). 7. All the internal angles of...

...angles, and their homologous sides are proportional (Euclid vL, Definition 1). 6. A line bisecting any angle of a triangle divides the opposite side into segments, which are in the same ratio as the remaining sides of the figure (Euclid vL 3). 7. All the internal angles of...

...of the product of several quantities equals the product of their like roots"; " The bisector of any angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides"; etc., are scarcely embraced in Comte's definition without an unjustifiable extension...

...of § 36 become when one of the angles is a right angle ? 2. Prove by means of the Law of Sines that the bisector of an angle 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 .4...

...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."...