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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. "
Elements of Geometry, Conic Sections, and Plane Trigonometry - Page 27
by Elias Loomis - 1877 - 443 pages
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Carpentry Made Easy: Or, The Science and Art of Framing, on a New and ...

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....
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

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...
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Elements of Geometry and Conic Sections

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...
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Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ...

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...
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Carpentry Made Easy, Or, The Science and Art of Framing, on a New and ...

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....
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

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...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

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...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

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...
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Elements of Geometry and Trigonometry: With Practical Applications

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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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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