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" If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects. "
Elements of Geometry...: Translated from the French for the Use of the ... - Page 142
by Adrien Marie Legendre, John Farrar - 1825 - 224 pages
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...it is greater than either of them. THEOREM X. 80. If two triangles have two sides and the inchided angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects. In the triangles ABC, DEF, let the side...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...triangle, the greater angle is opposite the greater side. 5. Spherical triangles are equal, (1) if they have two sides and the included angle of the...respectively equal to two sides and the included angle of the other; (2) if they have a side and two adjacent DEFLATION'S. 1. A Lune is a portion of the surface...
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Exercises on the geometry and measurement of plane figures, being solutions ...

Richard Wormell - Geometry, Plane - 1883 - 208 pages
...those of the second ; and let LA = L E. Draw the diagonals BD, FH. The triangles ABD, EFH , having two sides and the included angle of the one respectively equal to two sides and the included angle of the other, are equal, and BD = F H. Then triangles B С D, FGH, having three sides of one respectively...
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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...NOTE. — Have pupils give demonstration, prolonging BD instead of AD. THEOREM XII. If two triangles have two sides and the included angle of the one,...respectively, equal to two sides and the included, angle of the other, they are equal throughout. The triangles ACB and DFE have AC, the ang. A, and AB respectively...
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The Eclectic School Geometry: A Revision of Evan's School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...pupils give demonstration, prolonging BD instead of AD. THEOREM XII. If two triangles have two aides and the included angle of the one, respectively, equal to two sides and the included angle of the other, they are equal throughout. Conceive the triangle ACB to move to the right till AB coincides...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 346 pages
...other, by Proposition IX., and B is equal to B'. The triangles ABC and A' B'C' have now been proved to have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, and are equal, by Proposition VI. PROPOSITION XI.—THEOREM. 27. If two angles of a triangle...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...side CA = side ZX ; and, finally, area ABC = area XYZ. Proposition 4. THEOREM — If two triangles have two sides and the included angle of the one,...respectively equal to two sides and the included angle of the other, then the triangles are identically equal, and of the angles those are equal which are...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...then consider on what previous work the statements to be proved depend. Theorem 1. If two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, the triangles are congruent. JC' B Given To prove Proof. 1. the A ABC, A'B'C' such that...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...consider on what previous work the statements to be proved depend. TRIANGLES. Theorem 1. If two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other. the triangles are congruent. B A' Given To prove Proof. 1. the A ABC, A'B'C' such that...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...moved about in space while two of its points remain fixed. PROPOSITION I. 62. Theorem. If two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, the triangles are congruent. Given C' A ( ' B A' c' the A ABC, A'B'C' such that c = c',...
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