 | Euclides - 1884 - 434 páginas
...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 - 1885 - 389 páginas
...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 of equal... | |
 | George Bruce Halsted - 1886 - 394 páginas
...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 of equal... | |
 | 1887 - 644 páginas
...AB" is " sq. on AB," and for "the rectangle contained by the straight lines AB, CD"is"rect. AB, CD." 1. If two triangles have two sides of the one respectively equal to two sides of the other and the included angles equal, the remaining sides shall be equal. 2. If two triangles have two sides of the... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 páginas
...and substituting EC for its equal ED, BE + EC > BD, or BC > BD. PROPOSITION XV.—THEOREM. 31. If two triangles 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.... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 332 páginas
...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 - 1887 - 346 páginas
...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 - 1889 - 80 páginas
...Three different cases may arise ; prove each. Proposition XXXII. A Theorem. 69. Conversely, if two triangles have two sides of the one 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... | |
 | James Wallace MacDonald - 1894 - 76 páginas
...triangle having sides equal to the sides of a given triangle. Proposition XXXI. A Theorem. 68. If two triangles have two sides of the one respectively equal to two sides of the other and the included angles unequal, the third side of the one having the greater angle will be longer than the... | |
 | Robert Baldwin Hayward - 1890 - 160 páginas
...Ex. 2. Hence prove VIII. 4 directly without the aid of the polar triangles. X. — Ambiguous Cases. 1 . 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 the angles opposite to the other pair of equal sides... | |
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If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. 
