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
| Webster Wells - Geometry, Plane - 1908 - 208 pages
...either of the opposite int. A.] (§ 8C) 3. Since 6 is an ext. Z of A ABE, PROP. XXVII. THEOREM 98. Any **point in the bisector of an angle is equally distant from the sides of the angle.** Construct any Z ABC. Draw BD, the bisector of Z ABC; from any point P in the bisector, draw lines PM... | |
| Webster Wells - Geometry - 1908 - 336 pages
...either of the opposite int. 4.] (§ 80) 3. Since b is an ext. Z of A ABE, PROP. XXVII. THEOREM 98. Any **point in the bisector of an angle is equally distant from the sides of the angle.** Construct any Z ABC. Draw BD, the bisector of ZABC; from any point P in the bisector, draw lines PM... | |
| Webster Wells - 1909 - 154 pages
...CD, respectively. Also drop perpendicular KT to YY1, and connect T with J and L. Then, TJ= TL. (Any **point in the bisector of an angle is equally distant from the sides of the angle.)** § 98. 2. Since MNą. to plane of AB and CD, Z KTJ= Z KTL = rt. Z. (If two planes are perpendicular... | |
| George William Myers - Mathematics - 1910 - 304 pages
...PE4=PF. QED 1. Repeat the proof taking P on the left of B D. PROPOSITION XI 213. Theorem: Any point on **the bisector of an angle is equally distant from the sides of the angle.** Prove. (See FYM, § 294.) Using this conclusion and Proposition X, what can be said about the location... | |
| Geometry, Plane - 1911 - 192 pages
...One question may be omitted. (In solving problems use for n the approximate value 3^.) 1. Prove that **every point in the bisector of an angle is equally distant from the sides of the angle.** State the converse of this proposition. Is this converse true? 2. Prove that an angle formed by two... | |
| United States. Office of Education - 1911 - 1154 pages
...angles of any polygon, made by producing the sides in succession, is four right angles. 2. Prove that **every point in the bisector of an angle is equally distant from the sides of the angle.** 3. Prove that the medians of a triangle intersect in a point which is twothirds of the length of each... | |
| Education - 1911 - 1030 pages
...angles of any polygon, made by producing the sides in succession, is four right angles. 2. Prove that **every point in the bisector of an angle is equally distant from the sides of the angle.** 3. Prove that the medians of a triangle intersect In a point which is twothirds of the length of each... | |
| Horace Wilmer Marsh - Mathematics - 1914 - 306 pages
...large angle by drawing a line from the vertex of the large angle to the opposite side. II THEOREM 13 **Every point in the bisector of an angle is equally distant from the sides of the angle.** Represent by solid lines the distances* specified, and demonstrate. II THEOREM 14 Write this theorem... | |
| John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...this. See also Ex. 7, § 49.) 74. We may now prove the following important proposition : Every point on **the bisector of an angle is equally distant from the sides of the angle.** In the figure let OE be the bisector of " ' E angle AOB, and let Pbe any point on OE. The distance... | |
| Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...the point is said to be equally distant from the lines. PROPOSITION XXIX. THEOREM 94. Every point hi **the bisector of an angle is equally distant from the sides of the angle.** Proof : A PBC and PDC are rt. A. In rt. A PBC and PDC, PC=PC (Iden.). ZPCB = ZPCD (Hyp.). .-. A PBC... | |
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