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" The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. "
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 125
1898 - 208 pages
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Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...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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Euclid simplified. Compiled from the most important French works, approved ...

John Reynell Morell - 1875 - 220 pages
...the sides of this angle. 16. The bisectors of the angles of a triangle meet at the same point. 17. If the bisector of the angle of a triangle divides the opposite side into two equal parts, this triangle is isosceles. 18. If through the point of intersection of the bisectors...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...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....
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Practical Plane Geometry and Projection: For Science Classes ..., Volume 1

Henry Angel - Geometry, Plane - 1880 - 362 pages
...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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Practical plane geometry and projection. [2 issues].

Henry Angel - 1880 - 360 pages
...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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The Dictionary of Education and Instruction: a Reference Book and Manual on ...

Henry Kiddle, Alexander Jacob Schem - Education - 1881 - 378 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...
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Yale Examination Papers

Yale University - 1892 - 200 pages
...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....
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...value in (2), 6' = <?* 4- c * + 2am. §3'7 §317 QED PROPOSITION XX. THEOREM 327 '. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the oilier two sides. GIVEN — in the triangle ABC, AD the bisector of the angle A. DC _AC DB~ AB To PROVE...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...= n* + 2am + ii1* +yy = a8 + 2ai>i + C*. §317 QED PROPOSITION XX. THEOREM 32 7. The bisector of an angle of a triangle divides the opposite side into segments •which are proportional to the other two sides. GIVEN— in the triangle ABC, AD the bisector of the angle A. DC AC - = - • DB AB...
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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...b* = ' = a' + c* + 2am. -\-m'+y1 = a §317 §317 QED PROPOSITION XX. THEOREM 327. The bisector of an angle of a triangle divides the opposite side into segments which are proport1onal to the other two sides. GIVEN — in the triangle ABC, AD the bisector of the angle A....
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