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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 greater than the included angle of the second, then the third side of the first is greater than the third side of the second. "
The Elements of Plane Geometry - Side 45
av Charles Austin Hobbs - 1899 - 240 sider
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Plane Geometry

William James Milne - 1899 - 258 sider
...DB ; that is, AB > DB or DE. Therefore, etc. QED Proposition XXXT 130. Construct two triangles that have two sides of one equal respectively to two sides of the other, but the third sides unequal. How do the angles opposite the third sides compare in size? Theorem. If two sides...
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Plane and Solid Geometry

William James Milne - 1899 - 398 sider
...its equal DH, AH+ HB>DB; that is, AB > Dn or DE. Proposition XXXI 130. Construct two triangles that have two sides of one equal respectively to two sides of the other, but the third sides unequal. How do the angles opposite the third sides compare in size ? Theorem. If two sides...
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The Essentials of Geometry

Webster Wells - 1899 - 424 sider
...altitude of an equilateral triangle is 3 ; find its area. 20. Two triangles are equivalent if they ^ have two sides of one equal respectively to two sides of the other, and the included angles supplementary. U^A — D' 21. One diagonal of a rhombus is five-thirds of the...
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Annual Report of the Commissioners ..., Volum 66

1900 - 650 sider
...being assigned to each. Dr. ALEXANDER, Head Inspector. Mr. CUSSEN, District Ins|>ector. * SECTION A. 1. If two triangles have two sides of one equal respectively to two sides of the other, and have also the angles included by those sides equal, the triangles are equal in every respect. Prove...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1902 - 394 sider
...(Compare Props. V and VIII.) 44 PROPOSITION XXX. THEOREM 128. If two triangles have two sides of the one equal respectively to two sides of the other,...first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. B ——- Hyp. In A...
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Plane Geometry

Arthur Schultze - 1901 - 260 sider
...one. (Compare Props. V and VIII.) PROPOSITION XXX. THEOREM 128. If two triangles have two sides of the one equal respectively to two sides of the other,...first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In & ABC and A'B'C'...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1901 - 394 sider
...one. (Compare Props. V and VIII.) PROPOSITION XXX. THEOREM 128. If two triangles have two sides of the one equal respectively to two sides of the other,...first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C'...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1901 - 396 sider
...one. (Compare Props. V and VIII.) PROPOSITION XXX. THEOREM 128. If two triangles have two sides of the one equal respectively to two sides of the other,...first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C'...
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Non-Euclidean Geometry

Henry Parker Manning - 1901 - 122 sider
...the second, the third side of the first is greater than the third side of the second; and conversely, if two triangles have two sides of one equal, respectively, to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side...
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Non-Euclidean Geometry

Henry Parker Manning - 1901 - 120 sider
...the second, the third side of the first is greater than the third side of the second; and conversely, if two triangles have two sides of one equal, respectively, to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side...
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