 | Elias Loomis - 1857 - 242 ページ
...angle BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to tne three sides of the other, each to each, the three angles will also '• be equal, each to each,... | |
 | William E. Bell - 1857 - 250 ページ
...are equal. Cor. 1. The diagonal of a parallelogram divides it into two equal triangles. Cor. 2. When two triangles have the three sides of the one equal to the three sides of the other, the angles opposite the equal sides are also equal, and the triangles themselves are equal. Cor. 3.... | |
 | W. Davis Haskoll - 1858 - 422 ページ
...be subtended by the greater side, and the lesser angle by the lesser side. Any two triangles having the three sides of the one equal to the three sides of the other, are equal, equilateral, and equiangular. Any two triangles having each an equal angle contained by... | |
 | Elias Loomis - 1858 - 256 ページ
...angle BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to trie three sides of the other, each tc each, the three angles will also be equal, each to each, and... | |
 | William E. Bell - 1859 - 226 ページ
...are equal. Cor. 1. The diagonal of a parallelogram divides it into two equal triangles. Cor. 2. "When two triangles have the three sides of the one equal to the three sides of the other, the angles opposite the equal sides are also equal, and the triangles themselves arc equal. Cor. 3.... | |
 | Horatio Nelson Robinson - 1860 - 470 ページ
...(Ax. 5). Hence the theorem ; the difference between any two sidei of a triangle, etc. THEOREM XXI. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the two triangles are eqml, and the equal angles are opposite the equal sides. In two triangles, as... | |
 | George Roberts Perkins - 1860 - 472 ページ
...parallelogram are equal, as in the case of a rhombus, we have AB = AD, and the two triangles AEB and AED will have the three sides of the one equal to the three sides of the other respectively, consequently they will be equal (T. XXV.), and the angle AEB = AED, that is, in a rhombus... | |
 | Euclides - 1861 - 464 ページ
...make a rectil. ¿. = я rcctil. ¿. DEM. 32, I. — I, VI.; 11, V.; 9, V.; 8, I.— Triangles having the three sides of the one equal to the three sides of the other, have the ¿.s equal which are contained by eq. sides. 4, I. If two д s have each two sides and their... | |
 | Benjamin Greenleaf - 1862 - 532 ページ
...equal to it ; hence the angle A must be greater than the angle D. PROPOSITION XVIII. — THEOREM. 80. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles themselves will be equal. Let the triangles ABC, DEF have the side AB equal to DE, А... | |
 | Benjamin Greenleaf - 1862 - 518 ページ
...mutually equilateral, they are equivalent. ELEMENTS OF GEOMETRY. Let ABC, DEF be two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, AB to DE, AC to DF, andCBtoEF; then their triangles will be equivalent. Let 0 he the pole of... | |
| |
If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
