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. Elements of Geometry - Page 9by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| William E. Bell - Bridge building - 1857 - 250 pages
...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
...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 - Bridges - 1859 - 226 pages
...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 - 470 pages
...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 - Geometry - 1860 - 472 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 - 464 pages
...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 - 532 pages
...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 - Geometry - 1862 - 518 pages
...coincide thnnighout (Art. 34, Ax. 14). Thus circles having equal radii are equal ; and triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. Equal figures are always similar ; but similar figures may be very unequal. BOOK IV.... | |
| Benjamin Greenleaf - Geometry - 1861 - 638 pages
...arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having tlffe three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the angle E 0 G (Prop.... | |
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