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" If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second. "
Plane and Solid Geometry - Page 45
by Arthur Schultze, Frank Louis Sevenoak - 1902 - 370 pages
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...DN+NC'>DC'. (Ax. 9) Comparing (2) and (3), DF> D0', or DF> AC. QED 115. Corollary. Conversely, if two triangles have two sides of the one equal respectively to two sides of the other, tut the third sides unequal, the angle opposite the greater of the unequal sides will be the greater....
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...Therefore, if two triangles have two sides of the one equal to two sides of the other, each to each, but the included angle of the first greater than the included angle of the second, the third side of the first will be greater than the third side of the second. QUERIES. 1. What is...
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 176 pages
...which lines drawn to each side of the triangle, parallel to the other side, shall be equal. 199. If two triangles have two sides of the one equal respectively to two sides of the other, and the angle contained by the two sides of the one the supplement of the angle contained by the two...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...equals be taken from equals, the remainders are equal.) .-. t\ABC ^ &DFG. THEOREM XXIV. 177. If two triangles have two sides of the one equal respectively to two sides of the other, and the angles opposite to one pair of equal sides equal, then the angles opposite to the other pair...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...angle of an equiangular triangle? 31 PROPOSITION XXIII. THEOREM. 86. If two triangles have two sides of one equal respectively to two sides of the other,...first greater than the included angle of the second, the third side of the first is greater than the third side of the second. In the triangles ABC and...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...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 equal respectively to two sides of the other, the included angle of the first is greater than, equal to, or less than, the included angle of the...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 272 pages
...equals the common ZA CB ; then Z BCH= Z .4 + Z 5. Ax. 3 QED PROPOSITION XXVII. THEOREM. 152. // two triangles have two sides of the one equal respectively...angle of the second, then the third side of the first will be greater than the third side of the second. 111 'the triangles ABC and ABE, let AB = AB, BC=...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...drawn from the vertex to the middle point of the third side. * Proposition 29. Theorem. 119. If two triangles have two sides of the one equal respectively...to two sides of the other, but the included angle in the first triangle greater than the included angle in the second, then the third side of the first...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...the vertex to the middle point of the third side. Proposition 29. Theorem. 119. If tii-o Iriunifle* have two sides of the one equal respectively to two sides of the, other, but the included angle in the first triangle greater than the included angle in the second, then the third side of the first...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...(Ax. 8) Much more . • . Z EFH > Z EHF. .-. EH>EF. 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...
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