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" If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects. "
An Elementary Geometry - Page 11
by William Frothingham Bradbury - 1872 - 110 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...triangle symmetrical with it ABD, in the same manner as two plane triangles are applied, when they have two sides and the included angle of the one respectively equal to two sides and the included angle of the other (36). Therefore all the parts of the triangle EFG will be equal to those of the triangle...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...triangle symmetrical with it ABD, in the same manner as two plane triangles are applied, when they have two sides and the included angle of the one respectively equal to two sides and the included angle of the other (36). Therefore all the parts of the triangle EFG will be equal to those of the triangle...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...triangle symmetrical with it ABD, in the same manner as two plane triangles are applied, when they have two sides and the included angle of the one respectively equal to two sides and the included angle of the other (36). Therefore all the parts of the triangle EFG will be equal to those of the triangle...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...AC : DF, and, by construction, AG = DE ; therefore AH = DF. The two triangles AGH, DEF, have the two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are consequently equal. But the triangle AGH is similar to ABC; therefore DEF is...
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Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - Geometry - 1836 - 242 pages
...conditions which determine such equality are comprised in the four following theorems. THEOREM VI. 38. If two triangles have two sides, and the included...two sides and the included angle of the other, the remaining sides and angles are respectively equal. This theorem appears to be self-evident (IjP).....
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 524 pages
...angle included between them, are given, there are sufficient data for constructing the triangle ; and if two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other — it being understood that it is not the sum...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 542 pages
...given, there are sufficient data for constructing the triangle ; 416 CONSTRUCTION OF TRIANGLE?. and if two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other — it being understood that it is not the sum...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...the four right angles, as by the successive angles ACB, BCD, DCE, ECF, FCA. PROPOSITION V. THEOREM. ' If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal....
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...triangle ABC, symmetrical to ABC. 452. Theorem. If two triangles on the same sphere, or on equal spheres, have two sides, and the included angle of the one respectively equal to the two sides and the included angle of the other, they are equal, or else they are symmetrical. Isosceles...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...triangle symmetrical with it ABD, in the same manner as two plane triangles are applied, when they have two sides and the included angle of the one respectively equal to two sides and the included angle of the other (36). Therefore all the parts of the triangle EFG will be equal to those of the triangle...
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