 | Thomas Lund - Geometry - 1854 - 520 pages
...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, William Guy Peck - Mathematics - 1855 - 628 pages
...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.... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...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... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...angle will 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
...also be equal, each to each, and the triangles themselves will be equal Let ABC, DEF be two triangles having the three sides of the one equal to the three sides of the other, viz. : AB equal to DE. BC to EF, and AC to DF ; then will the three angles also be equal, viz. : the... | |
 | William E. Bell - Bridge building - 1857 - 250 pages
...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.... | |
 | William E. Bell - Bridges - 1859 - 226 pages
...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 - Geometry - 1860 - 470 pages
...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 ABC... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...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 pages
...line to 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... | |
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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. 
