 | 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.... | |
 | George Albert Wentworth - 1881 - 266 pages
...many sides has the polygon the sum of whose exterior angles is double that of its interior angles t I. 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. 8. BA... | |
 | 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... | |
 | 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...bisector, is nearer that side toward which it lies. 2. If the sum of two opposite angles of a quadrilateral is equal to two right angles, the vertices... | |
 | 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.... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...its perpendicular on any one of the three given lines as radius, will touch all three. PROOF. By 186, every point in the bisector of an angle is equally distant from its arms ; 416. The four tangents common to two circles occur in two pairs intersecting on the common... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...to one half the sum of the other two angles. IV. THEOREM. — Show that any point in the bisectrix of an angle is equally distant from the sides of the angle. V. THEOREM. — If two sides of a triangle are prolonged beyond the third side, show that the bisectrices... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...the base of an isosceles triangle to the opposite sides are equal. PROPOSITION XXX. THEOREM. 98. Any point in the bisector of an angle is equally distant from the sides of the angle. /A N Let BD be the bisector of the angle ABC and let P be any point in BD. To prove that P is equally... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...its perpendicular on any one of the three given lines as radius, will touch all three. PROOF. By 186, every point in the bisector of an angle is equally distant from its arms ; 416. The four tangents common to two circles occur in two pairs intersecting on the common... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...point not on the perpendicular is unequally distant from the extremities of the line. PROPOSITION XIX. 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; that is,... | |
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Every point in the bisector of an angle is equally distant from the sides of the angle... 
