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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

## The Elements of Plane and Solid Geometry: With Numerous Exercises

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...

## The Elements of Plane and Solid Geometry: With Numerous Exercises

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...

## Plane and Solid Geometry

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....

## Elementary Geometry

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...

## Exercises in Stewart's Plane and Solid Geometry: With Solutions for Teachers

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...

## An Examination Manual in Plane Geometry

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...

## Plane and Solid Geometry: Suggestive Method

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...

## The Elements of Geometry

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...