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" Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle. "
Elements of Geometry - Page 72
by George Albert Wentworth - 1881
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...parallelograms, we have Ab = A'B', Bo = B'C', Cd — C'D'; therefore, PROPOSITION XXXIX.— THEOREM. 126. Every point in the bisector of an angle is equally...is unequally distant from the sides of the angle. 1st. Let AD be the bisector of the angle SAC, Pany point in it, and PE, PF, the perpendicular distances...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...= A'B', Be — B'C', Cd — C'D'; therefore, AB' = B'C' = C'D'. PROPOSITION XXXIX.— THEOREM. 126. Every point in the bisector of an angle is equally...the angle ; and every point not in the bisector, but ivithin the angle, is unequally distant from the sides of the angle. 1st. Let AD be the bisector of...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...Ab = A'B', Be = B'C', Cd = C'D'; therefore, A'B' = B'C' = C'D'. PROPOSITION XXXIX.— THEOREM. 126. Every point in the bisector of an angle is equally...is unequally distant from the sides of the angle. 1st. Let AD be the bisector of the angle BA C, P any point in it, and PE, PF, the perpendicular distances...
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Key to Bradbury's Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 88 pages
...the centre, and DF the radius, of the required circumference. For, as shown in (16), a line bisecting an angle is equally distant from the sides of the angle, and hence С Е, В F are tangents to the circumference whose radius is DF and centre Z>. BOOK VI. It С...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 428 pages
...of section are symmetric to the bisectrix, and conversely. THEOREM 10. Each point of the bisectrix of an angle is equally distant from, the sides of the angle, Let ABC be an angle and B 0 its bisectrix. From any point O of the bisectrix BO let there be drawn...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 390 pages
...parallelograms, we have Ab = A'B', Be — B'C', Cd = C'D'; therefore, PROPOSITION XXXIX.— THEOREM. 126. I/very point in the bisector of an angle is equally distant...; and every point not in the bisector, but within th& angle, is unequally distant from the sides of the angle. 1st. Let AD be the bisector of the angle...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...Sphere. GEOMETRY. SKPTEMBEK, 1883. [State what text-book you have studied, and to what extent.] 1. Every point in the bisector of an angle is equally...distant from the sides of the angle; and every point within the angle, but not on the bisector, is nearer that side toward which it lies. 2. If the sum...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...is parallel to the bases, and equal to one-half their sum. (?) 105. Proposition XLVII.— Theorem. Every point in the bisector of an angle is equally distant from the sides of the angle. Let E be any point of AD, the bisector of the angle BAC, and EF, EG, the perpendiculars from E to AB,...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...many sides has the polygon the sum of whose exterior angles is double that of its interior angles t 7. Every point in the bisector of an angle is equally...a triangle having the angle B double the angle A. If BD bisect the angle B, and meet AС in D, show that BD is equal to A D. 9. If a straight line drawn...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...sides has the polygon the sum of whose exterior angles is double that of its interior angles t Ч 7. Every point in the bisector of an angle is equally...BA С is a triangle having the angle B double the an "le A. If BD bisect the angle B, and meet A С in D, show that BD is equal to A D. 9. If a straight...
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