 | Euclides - 1884 - 434 pages
...construction as in the text, but let A DEO fall on the other side of DE. PROPOSITION 25. THEOREM. If two triangles have two sides of the one respectively equal to two sides of the other, but their bases unequal, the angle contained by the two sides of the triangle which has the greater... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...opposite equal sides are equal.) But £ BDA -f 2£ ^C = st. £, = st. :£. 178. COROLLARY I. If two triangles have two sides of the one respectively equal to two sides of the other, and the angles opposite to one pair of equal sides equal, then, if one of the angles opposite the other pair... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...angles opposite equal sides are equal.) But £ BDA + 4 BDC = st. £, = st. . 178. COROLLARY I. If two triangles have two sides of the one respectively equal to two sides of the other, and the angles opposite to one pair of equal sides equal, then, if one of the angles opposite the other pair... | |
 | 1887 - 644 pages
...another, the side opposite the former shall be greater than the side opposite the latter. 2. If two triangles have two sides of the one respectively equal...two sides of the other, and the third side of the one greater than the. third side of the other, the angle opposite the former shall be greater than... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...triangle which has the greater included angle has the greater third side. PROPOSITION XV. If two triangle* have two sides of the one respectively equal to two sides of the other, and the third sides unequal, the triangle which has the greater third side has the greater included angle. PROPOSITION... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...than BC, by Proposition XII. Therefore C is greater than A. PROPOSITION XIV.— THEOREM. 30. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...than BC, by Proposition XII. Therefore C is greater than A. PROPOSITION XIV.—THEOREM. 30. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...k IS EXERCISES ON BOOK IV. -f ( • ' \ [-:-" u3 THEOREMS. 1. Two" triangles are equivalent if they have two sides of the . one respectively equal to two sides of the other, and the included angle of the one equal to the supplement of the included angle of the other. 2. The two opposite... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...the triangle which has the greater included angle has the greater third side. PROPOSITION XV. If two triangles have two sides of the one respectively equal to two sides uf the cither, and the third sides unequal, the triangle which has the greater third side has the greater... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...the other. SCHOLIUM. Three different cases may arise ; prove each. Proposition XXXII. A Theorem. 69. Conversely, if two triangles have two sides of the...respectively equal to two sides of the other and the included angles unequal, the angle opposite the longer third side will be greater than the angle opposite... | |
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... to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side of the first is. 
