 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....  Elements of Plane and Solid Geometry - Page 53by Alan Sanders - 1908 - 384 pagesFull view - About this book
 | George Albert Wentworth - 1879 - 196 pages
...inequalities, BD _f. DC< AB .f AC. Ex. 2. On the same sphere, or on equal spheres, if two spherical 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... | |
 | Eli Todd Tappan - Geometry - 1868 - 454 pages
...UNEQUAL TRIANGLES. 293. Theorem. — When two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third side in that triangle which has the greater angle, is greater than in the other. Let BCD and AEI be... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...parallelogram ; E and F the middle points of AB and CD. BF and ED trisect the diagonal A G. 104. If two triangles have two sides of the one equal respectively...to two sides of the other, and the included angles supplementary, the triangles are equivalent. 105. The diagonals divide a parallelogram into four equivalent... | |
 | George Albert Wentworth - 1881 - 266 pages
...QED Ex. Show that an equiangular triangle is also equilateral. PROPOSITION XXXI. THEOREM. 115. 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... | |
 | 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.... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...OF PLANE GEOMETRY. THEOREM XXVII. 89. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles...third sides are unequal, and the greater third side is in the triangle having the greater included angle. In the As ABC and DEF, let AC = DF, С B = FE,... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...sides. PROPOSITION VIII. 307. Theorem.—Ift wo triangles have two sides of the one respectively equal to two sides of the other, and the included angles...to the triangle having the greater included angle. DEMONSTRATION. Let ABC and DEF (Fig. 149) be two triangles having AC = DF, CB = FE, and C > F. Make... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...if two spherical triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the third sides are...to the triangle having the greater included angle. Conversely, If the two sides are equal, each to each, and the third sides unequal, the angles included... | |
 | 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 sides... | |
 | Public schools - 1884 - 634 pages
...right triangle is equivalent to the sum of the squares on the other two sides. 7. Prove that 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... | |
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