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. The Essentials of Geometry (plane) - Page 39by Webster Wells - 1898 - 242 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 - 1876 - 268 pages
...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 - 416 pages
...be equal respectively to two sides of another Л, but the included ¿ of the first be greater than **the included Z of the second, the third side of the first** will be greater than the third side of the second.) But both these conclusions are contrary to the... | |
| 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... | |
| 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... | |
| George Albert Wentworth - 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... | |
| 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... | |
| 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... | |
| Webster Wells - Geometry - 1886 - 392 pages
...there in each angle of an equiangular triangle? 31 PROPOSITION XXIII. THEOREM. 86. 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, the third side of the first is greater... | |
| 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... | |
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