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. Solid Geometry - Page 435by Claude Irwin Palmer - 1918 - 177 pagesFull view - About this book
| George Peacock - Algebra - 1830 - 732 pages
...involving them) and also tor the third jf we should take, therefore, as in Geometry, two triangles which have two sides of one equal respectively to two sides of the other, and the included angles equal, then the respective equality of the remaining angles in each triangle... | |
| Richard Wormell - Geometry, Modern - 1868 - 286 pages
...the triangles are unequal (fig. 79). When two triangles have two sides of the one respectively equal to two sides of the other, but the included angle of the one greater than the included angle of the other, the base of that which has the greater angle is greater... | |
| Richard Wormell - 1876 - 268 pages
...second. 2nd. Example. — A similar series of propositions occurs again in Theorems V. and XIII. " When two triangles have two sides of one equal respectively to two sides of the other," and — (a) " The included angle of the one equal to the included angle of the other, the base of one... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...triangle is also equilateral. PROPOSITION XXXI. THEOREM, 115. lf two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of thefirst greater than the included angle of the second, then the third side of the first will be greater... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...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 - 1879 - 196 pages
...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... | |
| George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...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... | |
| Public schools - 1884 - 634 pages
...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
...sphere until it coincides with ABC. THEOREM VI. 689. 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... | |
| George Bruce Halsted - Geometry - 1886 - 394 pages
...with ABC. TWO-DIMENSIONAL SPHERICS. THEOREM VI. 689. 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... | |
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