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 72by George Albert Wentworth - 1881 - 250 pagesFull view - About this book
| Edward Albert Bowser - Geometry - 1890 - 420 pages
...! to BC and passing through the mid. pt. of the J_ from A to BC. Proposition 4O. Theorem. 160. (1) **Every point in the bisector of an angle is equally distant from the sides of the angle; and** (2), conversely, even] point within an angle, and equally distant from its sides, is in the bisector... | |
| Edward Albert Bowser - Geometry - 1891 - 424 pages
...and produce it to meet BC in E. Then Q is the mid. pt. of AE. (154) Proposition 4O. Theorem. 160. (1) **Every point in the bisector of an angle is equally distant from the sides of the angle** j and (2), conversely, evenI point within an angle, and equally distant from its sides, is in the bisector... | |
| Seth Thayer Stewart - Geometry - 1891 - 428 pages
...following : 1. i. Parallel straight lines are everywhere equally distant. 2. Every point in the bisectrix **of an angle is equally distant from the sides of the angle.** 3. Two equal straight lines drawn from a point to a straight line make equal angles with that line.... | |
| William Chauvenet - 1893 - 340 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... | |
| Seth Thayer Stewart - Geometry - 1893 - 262 pages
...the distances AD and В С are equal. (Or, simply by red. ad. abs.) 2. Every point in the bisectrix **of an angle is equally distant from the sides of the angle.** I. From any point in the bisectrix, let fall _Lsupon the sides. 2. The JS are equal, being corresponding... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...construct a polygon similar to a given polygon. 6. To inscribe a regular decagon in a given circle. 7. **Every point in the bisector of an angle is equally...is unequally distant from the sides of the angle.** COLUMBIA COLLEGE, June, 1892. 1. Prove that, in any triangle, the greater side is opposite the greater... | |
| George Clinton Shutts - Geometry - 1894 - 412 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 ON are _L to AB and А С respectively. . § 131. Prove OM equal to О N. RECTILINEAR... | |
| Webster Wells - Geometry - 1894 - 394 pages
...O. Then since O is in the bisector AD, it is equally distant from the sides AB and A C. [Any p'(int **in the bisector of an angle is equally distant from the sides of the angle.]** (§ 99.) In like manner, since O is in the bisector BE, it is equally distant from the sides ^4B and... | |
| George D. Pettee - Geometry, Modern - 1896 - 272 pages
...B<2,AC<1 3 (preceding theorem), (contradicts hyp.) 38 PLANE GEOMETRY PROPOSITION XXIV 101. Theorem. **Every point in the bisector of an angle is equally distant from the sides.** Appl. Cons. Dem. B PC DB bisects ABC. Prove P = dist. from sides Draw PE and PF J- to sides of Z. rt.... | |
| Frederick Harold Bailey - Geometry, Analytic - 1897 - 392 pages
...bisector since it does not pass through the angle including the origin. We know by Plane Geometry that **every point in the bisector of an angle is equally distant from the sides of the angle.** Therefore, if (x, y) is any point of bisector (1), we have, by §32, x cos ^ -(- y sin 0.i — p i... | |
| |