 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 Geometry - Page 33by Edith Long, William Charles Brenke - 1916 - 276 pagesFull view - About this book
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...triangle is also equilateral. 50 (1EOMKTRY. BOOK I. PROPOSITION XXXI. THEOREM. 115. If two triangles hare two sides of the one equal respectively to two sides of the oiher, but the included angle of the first greater than the included angle of the second, then the... | |
 | 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 of the... | |
 | 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... | |
 | 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 of the... | |
 | 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.... | |
 | 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... | |
 | 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 of the... | |
 | 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... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...>BF'. That is, BOEF. PROPOSITION XXIV. THEOREM. 87. 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 included angle of the first is greater than the included... | |
 | 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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