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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: With Practical Applications to Mensuration - Page 59
by Benjamin Greenleaf - 1863 - 320 pages
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Elements of Geometry and Conic Sections

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

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

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

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

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

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

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

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

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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