| Elias Loomis - Conic sections - 1858 - 234 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... | |
| W. Davis Haskoll - Civil engineering - 1858 - 324 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... | |
| William E. Bell - Bridge building - 1857 - 254 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 - 224 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 - 453 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... | |
| George Roberts Perkins - Geometry - 1860 - 443 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
...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... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 pages
...hence the angle BAC is greater than ABC. PROPOSITION XVII. — THEOREM. Let ABC, DBF bo two triangles, **having the three sides of the one equal to the three sides of the other, each to each,** namely, AB to DE, F / ACtoDF, andCB toEF; then their triangles will bo equivalent. Let 0 be the pole... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...are 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
...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... | |
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