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" The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle, and likewise the externally. "
The New Zealand University Calendar - Page 70
by University of New Zealand - 1904
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...internally at M into AM and MB, and is divided externally at N into AN and NB. 189. Theorem. — The bisector of an angle of a triangle divides the opposite side internally into segments proportional to the adjacent sides. D B Hypothesis. In A ABC, CD bisects Z ACB. Conclusion....
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Plane Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 576 pages
...explain the results? SEGMENTS MADE BY THE BISECTOR OF AN ANGLE OF A TRIANGLE 317. THEOREM 106. The bisector of an angle of a triangle divides the opposite side internally into segments that have the same ratio as the other two sides of the triangle. O * A FIG. 322 Hypothesis:...
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Calendar

University of Allahabad - 1921 - 1018 pages
...to each other. The internal bisector of an angle of a triangle divides the opposite sides internal in the ratio of the sides containing the angle and...bisector externally. The ratio of the areas of similar triangle is equal to the ratio of the squires on corresponding sides. The following books are suggested...
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Calendar

University of Allahabad - 1922 - 1024 pages
...triangle and to each other. The internal bisector of an angle of a triangle divides the oppasite sides internally in the ratio of the sides containing the...likewise the external bisector externally. The ratio cf the areas of similar triangles is equal to the ratio of the squares on corresponding sides. The...
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Solid Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...tangent is a mean proportional between the whole secant and its external segment. THEOREM 106. The bisector of an angle of a triangle divides the opposite side internally into segments that have the same ratio as the other two sides of the triangle. THEOREM 107. The bisector...
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...direction of AB as positive and the direction of BA as negative, then AP + PB — AB. 359. Theorem. The bisector of an angle of a triangle divides the opposite side internally into segments proportional to the adjacent sides. D FIG. 358 B Given the triangle ABC, with angle x...
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Conditions of Recognition, Classification, and Payment of Teachers in the ...

Teachers - 1923 - 264 pages
...circles (or, in the same circle), angles at the centre and sectors are as the arcs on which they stand. The internal bisector of an angle of a triangle divides...angle, and likewise the external bisector externally. If two triangles are equiangular their corresponding sides are proportional : and the converse. If...
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Theoretical Geometry: Based on the Various Geometry Books by Godfrey and Siddons

Arthur Warry Siddons, Reginald Thomas Hughes - Geometry - 1926 - 202 pages
...squares on corresponding sides .... 118 NOTE ON THE RATIO OF AREAS OF TRIANGLES .... 118 THEOREM 58 (i). The internal bisector of an angle of a triangle divides...internally in the ratio of the sides containing the angle ........ 118 THEOREM 58 (ii). The external bisector of an angle of a triangle divides the opposite...
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Geometry: A Comprehensive Course

Daniel Pedoe - Mathematics - 1988 - 468 pages
...CA and deduce that PQ is equally inclined to AB and DC. 5.5 Deduce from the previous Exercise that the internal bisector of an angle of a triangle divides the opposite sides in the ratio of the sides containing the angle. 6.1 Reciprocal figures Theorem If A BC, PQR are...
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The Bombay University Calendar, Volume 1

University of Bombay - 1918 - 654 pages
...equal angles being homologous, the third angles of the triangles are either equal or supplementary. The internal bisector of an angle of a triangle divides...angle, and likewise the external bisector externally. In a right-angled triangle the perpendicular drawn from the right angle to the base will divide the...
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