 If two triangles have two sides of the 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.  Treatise on Elementary Geometry - Page 184by William Chauvenet - 1905Full view - About this book
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...III on I, Reflex ZAB3C>ZCB3A>ZCB1A. 7. But ZB1B3C =ZCB1B3. 8. .'.ZABuB1 >ZB3BlA. Theorem 11. If two triangles have two sides of the one respectively equal to two sides of the other, bat the third sides unequal, then the included angles are unequal, the greater angle being opposite... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...placed among the axioms to be memorized, but it is equally an axiom nevertheless. ] Theorem 10. 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... | |
 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...should lay off RH equal to RF and draw PH, we would have two A PRF and PRH having two sides of one equal to two sides of the other and the included angles unequal, and (Ex. 3 at the end of Chapter III.) the third side PH would be greater than the third side PF. FIG.... | |
 | 1898 - 830 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... | |
 | 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,...greater included angle has the greater third side. If two triangles have two sides of one respectively equal to two sides of the other, and the third... | |
 | 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... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 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... | |
 | 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... | |
 | 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 triangles... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...identically equal. PROPOSITION XX 79. If two triangles have two sides of the one equal, respectively, to two sides of the other, and the included angles...triangle which has the greater included angle has also the greater third side. Let ABC and A'B'C' be the two given triangles in which the side AB equals... | |
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