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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 triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second. "
Plane and Solid Geometry - Page 45
by Arthur Schultze, Frank Louis Sevenoak - 1902 - 370 pages
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...direction. To prove the proposition by the help of the construction we must know, — 1. That if two AS have two sides of the one equal respectively to two sides of the other, and also the ^ included between the said sides in the first A equal to the ^ included between the said...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...equiangular triangle is also equilateral. OEOMETRY. BOOK I. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively...two sides of the other, but the included angle of tlie first greater than the included angle of the second, then the third side of the first will be...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...equiangular triangle is also 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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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 436 pages
...of the other two sides of the triangle. 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, hut the included angle of the first greater than the included angle of the second, then the third side...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...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 than the third side of the second. B E la the AAB С and ABE, let AB = AB, but Z ABO...
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Harvard Examination Papers

Robert Fowler Leighton - 1877 - 372 pages
...that when 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 is greater than the third side of the second. 3. Show how to draw a tangent...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...triangle is also equilateral. 50 (1EOMKTRY. BOOK I. PROPOSITION XXXI. 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...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 196 pages
...inequalities, BD _f. DC< AB .f AC. Ex. 2. On the same sphere, or on equal spheres, if two spherical triangles have two sides of the one equal respectively...angle of the second, then the third side of the first will be greater than the third side of the second. In the spherical A ABC and A'B'C, let AB = A'B',AC...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...parallelogram ; E and F the middle points of AB and CD. BF and ED trisect the diagonal A G. 104. If two triangles have two sides of the one equal respectively to two sides of the other, and the included angles supplementary, the triangles are equivalent. 105. The diagonals divide a parallelogram...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...QED Ex. Show that an equiangular triangle is also equilateral. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively...angle of the second, then the third side of the first will be greater than the third side of the second. BB В In the А ABC and ABE, let AB = AB, BC —...
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