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" If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. "
The Elements of Plane Geometry - Side 45
av Charles Austin Hobbs - 1899 - 240 sider
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A Treatise on Algebra

George Peacock - 1830 - 685 sider
...involving them) and also tor the third jf we should take, therefore, as in Geometry, two triangles which have two sides of one equal respectively to two sides of the other, and the included angles equal, then the respective equality of the remaining angles in each triangle...
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PLANE AND SOLID GEOMETRY

GEORGE R. PERKINS - 1856
...THEOREM XXI. If two triangles have two sides of the one respectively equal to two sides of the other, and 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. FIRST BOOK. In the two triangles ABC and DEF, suppose...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 443 sider
...XXI. If two triangles have two sides of the one respectively equal to two sides of the other, and, the included, angle of the first greater than the included angle of the second, th'> third side of the first will be greater than the third side of the second. In the two triangles...
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An Elementary Course of Plane Geometry

Richard Wormell - 1868 - 261 sider
...the triangles are unequal (fig. 79). When two triangles have two sides of the one respectively equal to two sides of the other, but the included angle of the one greater than the included angle of the other, the base of that which has the greater angle is greater...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...second. 2nd. Example. — A similar series of propositions occurs again in Theorems V. and XIII. " When two triangles have two sides of one equal respectively to two sides of the other," and — (a) " The included angle of the one equal to the included angle of the other, the base of one...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 sider
...THEOREM. 115. If two triangles hare two sides of the one equal respectively to two sides of the oiher, but the included angle of the first greater than the included angle of the second, then the third siile of the ftrsl will be greater than the third side nf the second. BDB In the AAB...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 sider
...triangle is also equilateral. PROPOSITION XXXI. THEOREM, 115. lf two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of thefirst greater than the included angle of the second, then the third side of the first will be greater...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 sider
...two spherical triangles have two sides of the one equal respectively to two sides of the other, hut the included angle of the first greater than the included angle of the second, then the third side of the first will be greater than the third side of the second. 3. To draw an •...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 sider
...equilateral. GEOMETRY. BOOK I. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle (f the first greater than the included angle of the second, then 1lie third side of the first will...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 182 sider
...AC. Ex. 2. On the same sphere, or on equal spheres, if two spherical triangles have two sides of the one equal respectively to two sides of the other,...first greater than the included angle of the second, then the third side of the first will be greater than the third side of the second. In the spherical...
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