...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...

...difference of the segments, is equal to the line. 60. The line bisecting any angle, interior or exterior, divides the opposite side into segments which are proportional to the adjacent sides. Let B be the bisected angle of a triangle ADC. Throusjh C draw a line parallel to the bisecting line...

...difference of the segments, is equal to the line. 60, The line bisecting any angle, interior or exterior, divides the opposite side into segments which are proportional to the adjacent sides. Let B be the bisected angle of a triangle ABC. Through C draw a line parallel to the bisecting line...

...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...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. How do you find...

...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...

...to the line. C / THEOREM XXV. 62. The line bisecting any angle of a triangle, interior or exterior, divides the opposite side into segments which are proportional to the adjacent sides. 1st. Let B, an interior angle of the „ triangle ABC, be bisected by BD; then AB:BC = AD:DC Through...

...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 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...

...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...