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 72by George Albert Wentworth - 1881Full view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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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