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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. "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 29
by George Roberts Perkins - 1856 - 235 pages
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...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...
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The Elements of Solid Geometry

Robert Baldwin Hayward - Geometry, Solid - 1890 - 160 pages
...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...
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The Foundations of Geometry

Edward Travers Dixon - Geometry - 1891 - 180 pages
...angle opposite to it would be the less (see above), whereas it is the greater. PROPOSITION XIII. If two triangles have two sides of the one respectively equal to two sides of the other, but the angle between the directions of those sides greater in the one triangle than in the other,...
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A Text-book of Geometrical Deductions

James Andrew Blaikie, William Thomson - Geometry - 1891 - 160 pages
...triangle 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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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...opposite these sides in the other, are equal in all their parts. (Same.) Corollary IV. Two triangles, with two sides of the one respectively equal to two sides of the other, the two angles opposite these sides, in each triangle, being both acute, or one acute and the other...
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Elementary Synthetic Geometry

George Bruce Halsted - Geometry - 1896 - 208 pages
...third, that cutting the axis is the greater. Proof. BA = BC + CA' ; BC+ CA > BA'. 304. Theorem. If two triangles have two sides of the one respectively equal to two sides of the other, but the included angles unequal, then that third side is the greater which is opposite the greater...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1892 - 508 pages
...be careful to give the authority for each step. 10 2. Under what conditions are two triangles, which have two sides of the one respectively equal to two sides of the other, equal to one another ? 14 3. Give the enunciation and construction of I. II. 14 4. Prove that the parallelograms...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...opposite the greater side is greater than the angle opposite the less side. PROPOSITION XIV. 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....
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...supplementary. 2. If two triangles have two sides of one equal respectively to two sides of the other, but the third side of the first greater than the third...side of the second, the included angle of the first is greater than the included angle of the second. 3. If the diagonals of a quadrilateral are equal,...
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Annual Report

1894 - 1174 pages
...if he had 8 less of each he would only have 6 geese for 7 ducks. How many had he of each ? 7. If two triangles have two sides of the one respectively equal to two sides of the other, but the contained • angles unequal, the base of the triangle which has the greater contained angle...
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