 If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. Given the spherical triangle ABC, with angle B equal to angle C. To prove that AC = AB. Proof. Let A A'B'C ' be the polar triangle...  Plane and Solid Geometry - Page 450by Fletcher Durell - 1911 - 546 pagesFull view - About this book
 | Enoch Lewis - Conic sections - 1844 - 234 pages
...angles AEG, AFG, likewise equal (8.1) ; that is, the spherical angles ABC, ACB, are equal. QED ART. 50. If two angles of a spherical triangle are equal, the sides opposite to them are also equal. 83 Making the same construction as in the last article, we have, as before,... | |
 | Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...are the same as the spherical angles DAB, DBA (Prop. 17) ; which are therefore also equal. PROP. XXV. If two angles of a spherical triangle a/re equal, the sides opposite them are also equal. Let ABC be a spherical triangle, of which the angles A and B are equal ; the sides... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...triangles. (?) 2. Symmetrical isosceles spherical triangles are equal. (?) 464. Proposition XX. — Theorem. If two angles of a spherical triangle are equal, the sides opposite these angles are equal, or the triangle is isosceles. For, let A'B'C' be the polar triangle of ABC, and denote the sides of... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...two symmetrical triangles. PROPOSITION XXVI. THEOREM. 747. If two angles of a spherical triangle be equal, the sides opposite these angles are equal, and the triangle is isosceles. In the spherical Л AB С, let ZB = Z С. We are to prove AC = AB. Let Л A' B' (7 be the polar Д... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...perpendicular to the base. 31. Cor. 2. An equilateral spherical triangle is equiangular. THEOREM XII. 32. If two angles of a spherical triangle are equal, the sides opposite are also equal. SPHERICAL GEOMETRY. the polar triangle are also equal (29); and therefore the corresponding... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...perpendicular to the base. 31. Cor. 2. An equilateral spherical triangle is equiangular. THEOREM XII. 32. If two angles of a spherical triangle are equal, the sides opposite are also equal. the polar triangle are also equal (29); and therefore the corresponding sides of the... | |
 | George Albert Wentworth - Geometry - 1885 - 424 pages
...two symmetrical triangles. PROPOSITION XXVI. THEOREM. 747. If two angles of a spherical triangle be equal, the sides opposite these angles are equal, and the triangle is In the spherical A ABC, let Z B = Z C. We are to prove AC = AB. Let ^A'B'C ' be the polar A of AA £... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...the angles opposite the equal sides are equal. Proposition XXXV. A Theorem. 72. If two angles of a triangle are equal, the sides opposite these angles are equal, and the triangle is isosceles. COROLLARY. An equiangular triangle is also equilateral. Proposition XXXVI. A Theorem. 73. If two sides... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...COROLLARY. An equilateral triangle is also equiangular. Proposition XXXV. A Theorem. 72. If two angles of a triangle are equal, the sides opposite these angles are equal, and the triangle is isosceles. COROLLARY. An equiangular triangle is also equilateral. Proposition XXXVI. A Theorem. 73. If two sides... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...Ex. 579. To circumscribe a circle about a given spherical triangle. PROPOSITION XXIV. THEOREM. 755. If two angles of a spherical triangle are equal, the...these angles are equal, and the triangle is isosceles. In the spherical triangle ABC, let angle B equal angle C. To prove AC^= AB. Proof. Let the A A'B'C'... | |
| |
