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" If two triangles have two sides of the 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.... "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 28
by George Roberts Perkins - 1856 - 235 pages
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Annual Report of the Commissioners ..., Volume 64

1898 - 844 pages
...triangle and the external bisector of the other base angle is equal to half the vertical angle. 6. If two triangles have two sides of the one respectively equal to two sides of the other, but their bases unequal, their vertical angles are unequal. Give a direct proof of this. 7. Prove geometrically...
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 224 pages
...PLANE. 1. 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. State and prove the...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 450 pages
...THEOREM. 91. 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, the third side of the first is greater than the third side of the second. ia E1^-\ Given, in A ABC and DEF, AB - DE, AC= DF,...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...Theorem. 60. 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, the third side of the first is greater than the third side of the second. D Hypothesis. In the A ABC and DEF, AB = DE, AC = DF,...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 382 pages
...proof is the same when B2 falls above A'JB1. ^ ^ — ' C? PROPOSITION XI. . A 78. Theorem. If two triangles have two sides of the one respectively equal to two sides of the other, but the third sides unequal, then the included angles are unequal, the greater angle being opposite...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...the section and the equal sides are equal angles are equal. equal. PROPOSITION X. 77. Theorem. If two triangles have two sides of the one respectively equal to two sides of the other, but the included angles unequal, then the third sides are unequal, the greater side being opposite...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...angle is greater than the side opposite the less angle. THEOREM V. If two triangles have two sides of one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side. If two...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

Education - 1900 - 898 pages
...the side PQ is greater than PI!, prove that the angle PKQ is greater than the angle PQR. 7. 2. If two triangles have two sides of the one respectively equal to two sides of the other, but the contained angles unequal, the l>ase of the triangle which has the greater contained angle shall...
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Knowledge, Belief and Certitude: An Inquiry with Conclusions

Frederick Storrs Turner - Knowledge, Theory of - 1900 - 500 pages
...consider the use of the law of Contradiction by Euclid. He takes two triangles which have two sides of one respectively equal to two sides of the other, and the included angles equal: on these data he argues that the third sides are equal. For supposing that one of the...
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Non-Euclidean Geometry

Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 116 pages
...Theorem. 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, the third side of the first is greater than the third side of the second; and conversely, if two triangles have two sides of NON-EUCLIDEAN...
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