 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...(594). 773. Corollary — The radius being the same, two spherical triangles are equal, 1st. When they have two sides and the included angle of the one respectively equal to those parts of the other, and similarly arranged; 2d. When they have one side and the adjacent angles... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...let the triangle ACE = the triangle DFE. Bisect ECB with CH, and draw HE. The triangles HCB and HCE have two sides and the included angle of the one, respectively equal to the corresponding parts of the other, whence HE = HB. Now AH + HE > AE; but AH + HE = AH + HB = AB.... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...let the triangle ACE = the triangle DFE. Bisect ECB with CH, and draw HE. The triangles HCB and HCE have two sides and the included angle of the one, respectively equal to the corresponding parts of the other, whence HE = HB. Now AH + HE > AE; but AH + HE = AH + HB = AB.... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...(A. 8). Hence, CB must be the prolongation of AC ; which was to be proved. PROPOSITION V. THEOREM. If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, the triangles will be equal in... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...(A. 8). Hence, CB must be the prolongation of AC ; which was to be proved. PROPOSITION Y. THEOREM. If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, the triangles will be equal in... | |
 | B. Marks - 1875 - 176 pages
...What do you think of the areas of the triangles ? a d I cef DEMONSTRATION. We wish to prove, that, // two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...it is greater than either of them. THEOREM X. 80. If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects. In the triangles ABC, DEF, let the side AB equal DE, AC equal... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...together be equal to the sum of all the angles BAC, CAD, etc., formed about A. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to •each, the two triangles will be... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...AF and FE are also equal (const.), and the angles AFC and EFB are equal (Prop. XVII.). Therefore the two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, and are every way equal (Prop.... | |
 | Eli Todd Tappan - Geometry - 1868 - 454 pages
...indifferently. TWO SIDES AND INCLUDED ANGLE. 284. Theorem — Two triangles are equal when they have two sidex and the included angle of the one, respectively equal to two sides and the included angle of the other. If the angle A is equal to D, and the side AB to the side DF, and AC to DE, then the... | |
| |
If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects. 
