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" ... if two triangles have two sides of one equal, respectively, to two sides of the other... "
Elements of Plane Geometry - Page 42
by William Herschel Bruce, Claude Carr Cody (Jr.) - 1910 - 263 pages
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A Treatise on Algebra

George Peacock - Algebra - 1830 - 732 pages
...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: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...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...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...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...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...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 - Geometry - 1885 - 389 pages
...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 - Geometry - 1886 - 394 pages
...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 - Geometry - 1890 - 418 pages
...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 - 208 pages
...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 - Geometry - 1894 - 150 pages
...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...the 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...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...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...the 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...
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