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" ... if two triangles have two sides of one equal, respectively, to two sides of the other... "
Plane Geometry - Page 131
by John Charles Stone, James Franklin Millis - 1916 - 278 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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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 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 - 210 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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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...until they meet, and find the areas of the two triangles of which the trapezoid is the difference. 171. If two triangles have two sides of one equal respectively to two sides of another and the included angles supplementary, the triangles are equal in area. PROPOSITION XI. THEOREM....
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 256 pages
...ft. 3 in., what is the homologous altitude of the second ? 21. Two triangles are equivalent when they have two sides of one equal respectively to two sides of the other, and the included angles supplementary. 22. One diagonal of a rhomhus is five-thirds of the other, and...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...50.) Whence, the point A falls at D. PROPOSITION XXVIII. THEOREM. 89. If two triangles have two aides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 398 pages
...are equal.] (66.) But, BH + Gif > BG. PROPOSITION XXIX. THEOREM. 90. (Converse of Prop. XXVIII.) If two triangles have two sides of one equal respectively to two shies of the other, but the third side of the first greater than thk third side of the second, the...
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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...BC'<BX+XC. Or BC'<BC. QED PROPOSITION XXVI. THEOREM 93. If two triangles have two sides of one equal to two sides of the other but the third side of the first greater than the third side of the second, then the angle opposite the third side of the first is greater than the angle opposite the third side...
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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...Proposition XXIV. does it matter in what order the sides are arranged ? PROPOSITION XXV. THEOREM 92, If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the...
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