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" ... if two triangles have two sides of one equal, respectively, to two sides of the other... "
The Elements of Plane Geometry - Side 46
av Charles Austin Hobbs - 1899 - 240 sider
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A Treatise on Algebra

George Peacock - 1830 - 685 sider
...involving them) and also tor the third jf we should take, therefore, as in Geometry, two triangles which have two sides of one equal respectively to two sides of the other, and the included angles equal, then the respective equality of the remaining angles in each triangle...
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PLANE AND SOLID GEOMETRY

GEORGE R. PERKINS - 1856
...Conversely. If two triangles have two sides of the one respectively equal to two sides of the other, and the third side of the first greater than the third side of the second, the included angle of the first will be greater than the included angle of the second. For, if the included...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 443 sider
...Conversely. If two triangles have two sides of the one respectively equal to two sides of the other, and the third side of the first greater than the third side of the second, the included angle of the first will be greater than the included angle of the second. For, if the included...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...second. 2nd. Example. — A similar series of propositions occurs again in Theorems V. and XIII. " When two triangles have two sides of one equal respectively to two sides of the other," and — (a) " The included angle of the one equal to the included angle of the other, the base of one...
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...triangle symmetrical to the first to be greater than the third side of the second triangle, and therefore the third side of the first greater than the third side of the second. 690. From 688 and 689, by 33, Rule of Inversion, if two spherical triangles have two sides of the one...
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The Elements of Geometry

George Bruce Halsted - 1886 - 366 sider
...triangle symmetrical to the first to be greater than the third side of the second triangle, and therefore the third side of the first greater than the third side of the second. 690. From 688 and 689, by 33, Rule of Inversion, if two spherical triangles have two sides of the one...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 sider
...BC. .-. BC > EF. QED Proposition 3O. Theorem. 120. Conversely, if two triangles have two sides of the one equal respectively to two sides of the other, but the third side of the first triangle greater than the third side of the second, then the included angle of the first triangle is...
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Manual of Plane Geometry: On the Heuristic Plan, with Numerous Extra ...

George Irving Hopkins - 1891 - 179 sider
...hypothenuse is equivalent to the sum of the polygons upon the other two sides. ADVANCE THEOREMS. 435. If two triangles have' two sides of one equal respectively to two sides of the other, and their included angles supplementary, the triangles are equivalent. 437. If through the middle point...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - 1894 - 138 sider
...1890. 1. Two angles whose sides are perpendicular each to each are either equal or supplementary. 2. If two triangles have two sides of one equal respectively...first greater than the third side of the second, the included angle of the first is greater than the included angle of the second. 3. If the diagonals of...
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The Elements of Geometry

Webster Wells - 1894 - 378 sider
...for GH its equal CH, we have EF. PROPOSITION XXIX. THEOREM. 90. (Converse of Prop. XXVIII.) If tivo triangles have two sides of one equal respectively...first greater than the third side of the second, the included angle of the first is greater than the included angle of the second. In the triangles ABC...
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