 Every point in the bisector of an angle is equidistant from the sides of the angle. Hyp. Z DAB = Z DAC and 0 is any point in AD. To prove 0 is equidistant from AB and AC. Draw OP _L AB and OP' _L AC, and prove the equality of the two triangles.  Plane and Solid Geometry - Page 54by Fletcher Durell - 1911 - 546 pagesFull view - About this book
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...Compare CB and BD. BD POINTS EQUIDISTANT FROM THE SIDES OF AN ANGLE 188. THEOREM XXX. (1) Every point on the bisector of an angle is equidistant from the sides of the angle; and (2) conversely, if a point is equidistant from the sides of an angle it lies on the bisector of the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...perpendicular to MN, PQ is called the distance of P from Mff. /M PROPOSITION XXVII. THEOREM 125. Every point in the bisector of an angle is equidistant from the sides of the angle. •c Given AD, the bisector of Z BAC, and O, any point in AD. To prove O is equidistant from AB and... | |
 | Werrett Wallace Charters - Education - 1923 - 498 pages
...fractions Addition of mixed numbers and common fractions Measuring linear magnitudes A point lying in the bisector of an angle is equidistant from the sides of the angle 3 1 1 1 2 1 1 1 1 1 2 1 1 18 3 1 2 2 7 2 6 4 2 1 1 2 4 1 3 1 4 2 282 TABLE II A COURSE OF STUDY IN... | |
 | Werrett Wallace Charters - Education - 1923 - 370 pages
...follow any time after the (*) sign, and the notation of mixed numbers have been taught. A point lying in the bisector of an angle is equidistant from the sides of an angle. This theorem should be stated as a fact, and need not be supported by a rigorous proof. Need... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...bisectors of the sides of a triangle meet in a point which is equidistant from the vertices. 16. Every point in the bisector of an angle is equidistant from the sides of the angle. 17. Every point equidistant from the sides of an angle is in the bisector of that angle. 18. The bisectors... | |
 | William Weller Strader, Lawrence D. Rhoads - Geometry, Plane - 1927 - 434 pages
...proved equal? (The pupil may complete the demonstration.) 103 Proposition 30 172. Theorem. Any point on the bisector of an angle is equidistant from the sides of the angle. Given: ¿ 1 = Z2, PA _L OA, PB _L OB, and P any point in OP. To prove: PA = PB. HINT: The distance... | |
 | Research & Education Association Editors, Ernest Woodward - Mathematics - 2012 - 1080 pages
...perpendicular to the radius OA, where O is at the center of the circle. (Problems 603 and 604) 4. Any point on the bisector of an angle is equidistant from the sides of the angle. (Problem 606) 5. The perpendicular bisectors of the sides of a triangle intersect in a point. (Problem... | |
 | James A. Simpson - Boundaries (Estates) - 2005 - 424 pages
...of an angle, it is on the bisector of the angle. The converse is, of course, also true: A point on the bisector of an angle is equidistant from the sides of the angle. After the boundary-bank bearings, distances and coordinates are known, the computation can proceed.... | |
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