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" Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides. "
Complete School Algebra - Page 464
by Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1919 - 507 pages
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...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...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 238 pages
...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...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...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...
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Elements of geometry, with ... trigonometry

André Darré - 1872
...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...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...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...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...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...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 346 pages
...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,...
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Practical plane geometry and projection. [2 issues].

Henry Angel - 1880
...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...
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Practical Plane Geometry and Projection: For Science Classes ..., Volume 1

Henry Angel - Geometry, Plane - 1880
...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...
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The Dictionary of Education and Instruction: a Reference Book and Manual on ...

Alexander Jacob Schem - Education - 1881 - 374 pages
...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 the signification...
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