| William E. Bell - Bridge building - 1857 - 254 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 - 324 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 - 234 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... | |
| Charles Davies, William Guy Peck - Mathematics - 1859 - 592 pages
...proposition we need the following, which have been before proved, viz : Prop X. (of Legcndre). " When **two triangles have the three sides of the one equal...each to each and the triangles themselves will be** cquci.." Prop. V. " When two triangles have two sid'-s, ami the included angle of the one equal lo... | |
| William E. Bell - Bridges - 1859 - 224 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 arc equal. Cor. 3.... | |
| Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...(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 ABC... | |
| George Roberts Perkins - Geometry - 1860 - 443 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... | |
| Euclides - 1861
...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 - Geometry - 1862 - 520 pages
...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... | |
| Benjamin Greenleaf - Geometry - 1862 - 514 pages
...equal spheres, are mutually equilateral, they are equivalent. £et ABC, DEF be two triangles, having **the three sides of the one equal to the three sides of the other, each to each,** namely, А В to DE, AC to DF, and С В to EF; then their triangles will be equivalent. Let 0 be the... | |
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