 If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.  A Text-book of Geometry - Page 44by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
 | 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.... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...equiangular triangle is also equilateral. GEOMETRY. BOOK I. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively...the second, then the third side of the first will be (/realer than the third side of the second. EE In the А AB С and ABE, let AB = AB, B С = BE; but... | |
 | 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... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...Therefore, if two triangles have two sides of the one equal to two sides of the other, each to each, but the included angle of the first greater than the included angle of the second, the third side of the first will be greater than the third side of the second. QUERIES. 1. What is... | |
 | George Albert Wentworth - Geometry - 1884 - 422 pages
...of the other two 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...the second, then the third side of the first will he greater than the third side of the second. 3. To draw an arc perpendicular to a given spherical... | |
 | 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...angle of the second, then the third side of the first is greater than the third side of the second. 8. Prove that if the middle points of the three sides... | |
 | 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
...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,...first greater than the included angle of the second, the third side of the first is greater than the third side of the second. In the triangles ABC and... | |
 | 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... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...drawn from the vertex to the middle point of the third side. * Proposition 29. Theorem. 119. If two triangles have two sides of the one equal respectively...to two sides of the other, but the included angle in the first triangle greater than the included angle in the second, then the third side of the first... | |
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