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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 - 250 pages
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...many sides has the polygon the sum of whose exterior angles is double that of its interior angles ? 7. Every point in the bisector of an angle is equally...unequally distant from the sides of the angle. 8. BAC is a triangle having the angle B double the angle A. If BD bisect the angle B, and meet AC in D,...
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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? < 7. Every point in the bisector of an angle is equally...is unequally distant from the sides of the angle. |'. fj 8. BA С is a triangle having the angle B double the angle A. If BD bisect the angle B, and...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...ABE and EBD> CBD (26) ; much more then isABC>CBD. THEOREM XXI. 103. Every point in a line bisecting an angle is equally distant from the sides of the angle ; and every point without the bisecting line but within the angle is unequally distant from tlie sides of the angle....
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 196 pages
...is double that of its interior angles? In this case 4 (— 2) = 4. .'. = 3. Ex. 7. Every pokit in the bisector of an angle is equally distant from...is unequally distant from the sides of the angle. I. Let A be the given Z, and AB its bisector. From any point in AB, as O, draw OC and OD _L to the...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...ABE and EBD> CBD (26); much more then isABC>CBD. THEOREM XXI. 103i Every point in a line bisecting an angle is equally distant from the sides of the angle; and every point without the bisecting line but within the angle is unequally distant from the sides of the angle. 1st....
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...from the extremities of a line lies upon the perpendicular bisector of the line. THEOREM XVIII. 106. 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. Hypothesis. MON,...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...or BO AB. (98) (Ax. 11) QED ELEMENTS OF PLANE GEOMETRY. BISECTORS OF ANGLES. THEOREM XXXV. 101. Any point in the bisector of an angle is equally distant from the sides of the angle. Let BF be the bisector of the Z. ABC, P any point in it, and PD and PE _Ls to AB and EC. To prove that...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1884 - 422 pages
...many sides has the polygon the sum of whose exterior angles is double that of its interior angles ? 7. Every point in the bisector of an angle is equally...angle, is unequally distant from the sides of the Jingle. 8. BA С is a triangle having the angle B double the angle A. If BD bisect the angle B, and...
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Yale Examination Papers

F. B. Stevens - Examinations - 1884 - 202 pages
...cylinder and sphere. September, 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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Euclid and His Modern Rivals

Lewis Carroll - Geometry - 1885 - 318 pages
...I. 29. I see several Propositions which might well be inserted as exercises on Euclid (eg Pr. xxxix, 'Every point in the bisector of an angle is equally distant from the sides '), but which are hardly of sufficient importance to be included as Propositions : and others (eg Pr....
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