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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. "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 44
των William Chauvenet - 1872 - 368 σελίδες
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...corresponding angles adjacent to these sides are equal (51), namely, BAb = CBc = DCd, and ABb = BCc = CDd; therefore, these triangles are equal to each...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...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...figures A'b, B'o, C'd, being parallelograms, we have Ab = A'B', Bo = B'C', Cd — C'D'; therefore, PROPOSITION XXXIX.— THEOREM. 126. Every point in...the angle. 1st. Let AD be the bisector of the angle SAC, Pany point in it, and PE, PF, the perpendicular distances of Pfrom AB and AC; then, PE = PF. For,...

Key to Bradbury's Elementary Geometry and Trigonometry

William Frothingham Bradbury - 1872 - 79 σελίδες
...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...

The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874
...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...

Report, Τόμοι 11-20

1876
...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...

Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - 1876 - 364 σελίδες
...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,...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...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...is unequally distant from the sides of the angle. 8. BA С is a triangle having the angle B double the an "le A. If BD bisect the angle B, and meet A...

An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - 1877 - 240 σελίδες
...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....

Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 182 σελίδες
...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...

An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - 1880 - 240 σελίδες
...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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