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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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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 254 pages
...a line- is equally distant from the extremities of the line. PROPOSITION XXIX. THEOREM. 121. I. Any point in the bisector of an angle is equally distant from the si/lcs nf the angle. II. Am/point outside tin 1 binector of an angle is unequally distant from the...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898 - 212 pages
...that of a cone whose base is a great circle of the sphere and whose altitude is R. JUNK 1889. P 1. Every point in the bisector of an angle is equally...is unequally distant from the sides of the angle. 2. To find the center of a given arc of a circle. 3. If three or more straight lines passing through...
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 228 pages
...of a cone whose base is a great circle of the sphere and whose altitude is R. JUNE 1889. PLANE. 1. Every point in the bisector of an angle is equally...is unequally distant from the sides of the angle. 2. To find the center of a given arc of a circle. 3. If three or more straight lines passing through...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...A ABE, Z DEC >ZA Then, since Z 5,0C is > Z ZXEC, and Z DEC> Z .4, PROP. XXXV. THEOREM. 101. .42/ point in the bisector of an angle is equally distant from the sides of the angle. /A. " N Given P, any point in bisector BD of Z ABC, and lines PM and P^J. to AB and BC, respectively....
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1898 - 250 pages
...a line is equally distant from the extremities of the line. PROPOSITION* XXIX. THEOREM. 121. I. Any point in the bisector of an angle is equally distant from the sides of the angle. II. Any point outside the bisector of an angle is unequally distant from the sides of the angle. 122....
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...equidistant from the extremities of a line is a line bisecting that line at right angles. THEOREM XV. Every point in the bisector of an angle is equally...of the angle ; and every point not in the bisector is unequally distant from the sides of the angle ; that is, the bisector of an angle is the locus of...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...straight line. (?) Then ABG is an isosceles A. (?) .-. A ABC =& DEF. (?) QED Proposition 45. Theorem. 56. Every point in the bisector of an angle is equally distant from the sides of the angle. Hypothesis. E is any point in AD, the bisector of Z BAC, and EF and EG are _L to AB and AC respectively....
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...A ABE, Z DEC > Z .4. Then, since Z SZK7 is > Z D-EC, and Z DC > ZA, PROP. XXXV. THEOREM. 101. Any point in the bisector of an angle is equally distant from the sides of the angle. Given P, any point in bisector BD of Z ABC, and lines PM and PN to AB and BC, respectively. To Prove...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 450 pages
...an ext. Z of A ABE, Then, since Z .BZK7 is > Z DEC, and Z D-EC > Z .4, PROP. XXXV. THEOREM. 101. Any point in the bisector of an angle is equally distant from the sides of the angle. /A N Given P, any point in bisector BD of Z ABC, and lines PM and PN to AB and AC, respectively....
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Plane and Solid Analytic Geometry: An Elementary Textbook

Charles Hamilton Ashton - Geometry, Analytic - 1902 - 306 pages
...(1) A,x. and (2) A,* and let (x', y') be any point on the bisector of the angle between them. Since every point in the bisector of an angle is equally distant from the sides, HP' and KP' are numerically equal. But Hence the relation which must exist between x' and y' in order...
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