 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 42by George Albert Wentworth - 1899 - 256 pagesFull view - About this book
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...triangle is also equilateral. GEOMETRY. BOOK I. 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 (f the first greater than the included angle of the second, then 1lie third side of the first will... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...sides of the triangle. 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, hut the included angle of the first greater than the included angle of the second, then the third side... | |
 | 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
...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 first will be greater than... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...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
...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 first will be greater than... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...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
...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
...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 first is greater than the... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...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... | |
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