 | George Bruce Halsted - Geometry - 1885 - 389 pages
...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... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...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... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...Exercise, and III., 43.) G k 13 EXERCISES ON BOOK IV. THEOEEMS. 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... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...28, Exercise, and III., 43.) 13 EXERCISES ON BOOK IY. 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... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...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... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...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... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...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 third sides unequal, the angle opposite the longer third side will be greater than the angle opposite... | |
 | Robert Baldwin Hayward - Geometry, Solid - 1890 - 160 pages
...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... | |
 | James Andrew Blaikie, William Thomson - Geometry - 1891 - 154 pages
...show AABD = AACD, AGBD = AGCD; .-. AGAB = AGCA; .-. their halves are equal, etc. 7. If two triangles have two sides of the one respectively equal to two sides of the other and the contained angles supplementary, the triangles shall be equal in area. 62 8. The diagonals of a... | |
 | James Andrew Blaikie, William Thomson - Geometry - 1891 - 160 pages
...which has the greater contained angle shall be greater than the base of the other. 25. If two triangles have two sides of the one respectively equal to two sides of the other but the bases unequal, the angle contained by the two sides of the triangle which has the greater base... | |
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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. 
