 | Thomas Lund - Geometry - 1854 - 520 pages
...Therefore the triangles coincide, and are equal, in all respects, as stated above. COR. Hence, also, if two triangles have the three sides of the one equal to the three sides of the other, each to each, in the same order, the two triangles will be equal, and their angles likewise will be equal, each to... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...hypothesis : therefore, BA C is greater than EDF. PROPOSITION X. THEOREM. If two triangles have ihe three sides of the one equal to the three sides of the other, each to each, the triangles are equal. Let EDF and BA C be two triangles, having the side ED=BA, the side EF=BC, and the side DF=AC;... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...proposition we need the following, which have been before proved, viz : Prop X. (of Legendre). " When two triangles have the three sides of the one equal...to the three sides of the other, each to each, the three angles will also be equal, each to each, and the triangles themselves will bo equal." Prop. V.... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...chord, and the arc AE equal to EB- ^ First- Draw the two radii CA, CBThen the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note- When reference is made from one theorem to another, in the same Book, the number of the theorem... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...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... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...results contradicts the hypothesis : therefore, BA C is greater than EDF. PROPOSITION X. THEOREM.' If two triangles have the three sides of the one equal...three sides of the other, each to each, the triangles are equal. Let EDF and BAC be two triangles, having the side ED=BA, the side EF=BC, and the side DF=AC\... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...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 - Bridge building - 1857 - 250 pages
...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 - Civil engineering - 1858 - 422 pages
...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 - Conic sections - 1858 - 256 pages
...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... | |
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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. 
