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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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Massachusetts State Normal Schools: Containing a Circular of Information, a ...

Teachers - 1901 - 258 pages
...principal in three years at 4 per cent. will amount to $448. Take either 1 or 2. 1. Prove that any point in the bisector of an angle is equally distant from the sides of the angle. 2. Prove that the line dividing two sides of a triangle proportionally is parallel to the third side....
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Elements of Plane Geometry

Alan Sanders - Geometry, Modern - 1901 - 260 pages
...of the rectangle is less than that of the rhomboid. PROPOSITION XXXVIII. THEOREM 230. Any point on the bisector of an angle is equally distant from the sides of the angle; and any point not on the bisector is unequally distant from the sides. BB Let ABC be any angle, BD its...
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Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...and ABE, is greater than angle A. Therefore angle BDC is greater than angle A. THEOREM XXV. 89. Any point in the bisector of an angle is equally distant from the sides of the angle. Let BD be the bisector of an angle, ABC, and let P be any point in B D. To prove that P is equally...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 396 pages
...less than that of the rhomboid. SANDERS' GEOM. — 5 PROPOSITION XXXVIII. THEOREM 230. Any point on the bisector of an angle is equally distant from the sides of the angle; and any point not on the bisector is unequally distant from the sides. Let ABC be any angle, BD its bisector,...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 392 pages
...of the rectangle is less than that of the rhomboid. PROPOSITION XXXVIII. THEOREM 230. Any point on the bisector of an angle is equally distant from the sides of tlie angle; and any point not on the bisector is unequally distant from the sides. BB Let ASC be any...
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Treatise on Elementary Geometry

William Chauvenet - 1905 - 336 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...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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Plane Geometry Suggestive Method

George Clinton Shutts - 1905 - 260 pages
...points without the _L from the extremities. 88. 4. What is the required locus ? Ex. 68. Prove that every point in the bisector of an angle is equally distant from the sides of the angle. Suggestion: OM and 0 N are _L to AB and AC respectively. 131. Prove OM equal to O N. PROPOSITION...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...point to two lines are equal, the point is said to be equally distant from the lines. 79. THEOREM. Every point in the bisector of an angle is equally distant from the sides of the angle. Given: Z ACE; bisector CQ; point P in C'Q; distances PB and To Prove : PH = Pii. Proof: A PBC and PDC...
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - Building - 1906 - 634 pages
...CD, that is, OC, which meets the bisectors AO and BO in O, is the bisector of the angle C. 101. Any point in the bisector of an angle is equally distant from the sides of the angle. For it has just been shown that, in Fig. 69, OF= O E. 102. The perpendiculars erected at the middle...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...point to two lines are equal, the point is said to be equally distant from the lines. 79. THEOREM. Every point in the bisector of an angle is equally distant from the sides of the angle. Given : Z ACE; bisector CQ; point P in CQ; distances PB and PD. To Prove : PB = PD. Proof : A PBC and...
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