 | 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.... | |
 | 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... | |
 | 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.... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...A ABE, Z DEC > Z .4. Then, since Z SZK7 is > Z D-EC, and Z D£C > 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... | |
 | 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.... | |
 | 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... | |
 | 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.... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...the rectangle is less than that of the rhomboid. 66 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. B Let ABC be any angle, BD its bisector,... | |
 | 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... | |
 | 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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Every point in the bisector of an angle is equally distant from the sides of the angle... 
