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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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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 208 pages
...either of the opposite int. A.] (§ 8C) 3. Since 6 is an ext. Z of A ABE, PROP. XXVII. THEOREM 98. Any point in the bisector of an angle is equally distant from the sides of the angle. Construct any Z ABC. Draw BD, the bisector of Z ABC; from any point P in the bisector, draw lines PM...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 336 pages
...either of the opposite int. 4.] (§ 80) 3. Since b is an ext. Z of A ABE, PROP. XXVII. THEOREM 98. Any point in the bisector of an angle is equally distant from the sides of the angle. Construct any Z ABC. Draw BD, the bisector of ZABC; from any point P in the bisector, draw lines PM...
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Key to the Exercises in Wells's New Geometry

Webster Wells - 1909 - 154 pages
...CD, respectively. Also drop perpendicular KT to YY1, and connect T with J and L. Then, TJ= TL. (Any point in the bisector of an angle is equally distant from the sides of the angle.) § 98. 2. Since MNą. to plane of AB and CD, Z KTJ= Z KTL = rt. Z. (If two planes are perpendicular...
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Second-year Mathematics for Secondary Schools, Volume 2

George William Myers - Mathematics - 1910 - 304 pages
...PE4=PF. QED 1. Repeat the proof taking P on the left of B D. PROPOSITION XI 213. Theorem: Any point on the bisector of an angle is equally distant from the sides of the angle. Prove. (See FYM, § 294.) Using this conclusion and Proposition X, what can be said about the location...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...One question may be omitted. (In solving problems use for n the approximate value 3^.) 1. Prove that every point in the bisector of an angle is equally distant from the sides of the angle. State the converse of this proposition. Is this converse true? 2. Prove that an angle formed by two...
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Bulletin, Issues 1-13

United States. Office of Education - 1911 - 1154 pages
...angles of any polygon, made by producing the sides in succession, is four right angles. 2. Prove that every point in the bisector of an angle is equally distant from the sides of the angle. 3. Prove that the medians of a triangle intersect in a point which is twothirds of the length of each...
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Bulletin, Issues 1-11

Education - 1911 - 1030 pages
...angles of any polygon, made by producing the sides in succession, is four right angles. 2. Prove that every point in the bisector of an angle is equally distant from the sides of the angle. 3. Prove that the medians of a triangle intersect In a point which is twothirds of the length of each...
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Constructive Text-book of Practical Mathematics, Volume 3

Horace Wilmer Marsh - Mathematics - 1914 - 306 pages
...large angle by drawing a line from the vertex of the large angle to the opposite side. II THEOREM 13 Every point in the bisector of an angle is equally distant from the sides of the angle. Represent by solid lines the distances* specified, and demonstrate. II THEOREM 14 Write this theorem...
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Plane Geometry

John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...this. See also Ex. 7, § 49.) 74. We may now prove the following important proposition : Every point on the bisector of an angle is equally distant from the sides of the angle. In the figure let OE be the bisector of " ' E angle AOB, and let Pbe any point on OE. The distance...
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Robbin's New Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...the point is said to be equally distant from the lines. PROPOSITION XXIX. THEOREM 94. Every point hi the bisector of an angle is equally distant from the sides of the angle. Proof : A PBC and PDC are rt. A. In rt. A PBC and PDC, PC=PC (Iden.). ZPCB = ZPCD (Hyp.). .-. A PBC...
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