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
| George Bruce Halsted - Geometry - 1885 - 389 pages
...its perpendicular on any one of the three given lines as radius, will touch all three. PROOF. By 186, **every point in the bisector of an angle is equally distant from** its arms ; 416. The four tangents common to two circles occur in two pairs intersecting on the common... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...to one half the sum of the other two angles. IV. THEOREM. — Show that any point in the bisectrix **of an angle is equally distant from the sides of the angle.** V. THEOREM. — If two sides of a triangle are prolonged beyond the third side, show that the bisectrices... | |
| Webster Wells - Geometry - 1886 - 392 pages
...the base of an isosceles triangle to the opposite sides are equal. PROPOSITION XXX. THEOREM. 98. Any **point in the bisector of an angle is equally distant from the sides of the angle.** /A N Let BD be the bisector of the angle ABC and let P be any point in BD. To prove that P is equally... | |
| George Bruce Halsted - Geometry - 1886 - 394 pages
...its perpendicular on any one of the three given lines as radius, will touch all three. PROOF. By 186, **every point in the bisector of an angle is equally distant from** its arms ; 416. The four tangents common to two circles occur in two pairs intersecting on the common... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 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... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 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... | |
| William Chauvenet - Geometry - 1887 - 364 pages
...on the perpendicular is unequally from the extremities of the line. PROPOSITION XIX. , J W ""T " , f **point in the bisector of an angle is equally distant from the** the angle; and every point not in the bisector, but within the , unequally distant from the sides of... | |
| William Chauvenet - Geometry - 1888 - 826 pages
...Be = B'C', Cd = C'D'; therefore, PROPOSITION XXXIX.— THEOREM. 126. Every point in the bisector o/ **an angle is equally distant from the, sides of the...is unequally distant from the sides of the angle.** 1st. Let AD be the bisector of the angle BA C, P any point in it, and PE, PF, the perpendicular distances... | |
| George Albert Wentworth - 1889 - 264 pages
...middle point of the IvaQ.^s" ^£&- Theorem. Every p'oint in the bisector of an angle is equidistant **from the sides of the angle, and every point not in the bisector** is unequally distant from the sides. 70. Theorem. The line joining the middle points of two sides of... | |
| George Albert Wentworth - 1889 - 276 pages
...through the middle point of the line. 69. Theorem. Every point in the bisector of an angle is equidistant **from the sides of the angle, and every point not in the bisector** is unequally distant from the sides. 70. Theorem. The line joining the middle points of two sides of... | |
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