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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 will be equal. "
Elements of Geometry and Conic Sections - Page 17
by Elias Loomis - 1857 - 226 pages
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...equal to the angle D (Post. 7) ; make AG equal to DE, and draw GC. Then will the triangles AGC and DEF have two sides and the included angle of the one equal...and the included angle of the other, each to each; consequently, GC is equal to EF (PV). Now, the point G may be without the triangle ABC, it may be on...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...and can be applied so as to coincide. PROPOSITION XT. 301. Theorem. — Two parallelograms having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are equal. DEM.— Let AC and EC be two parallelograms, with AD = EH, AB = EF, and A = E ; then are...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...and can be applied so as to coincide. PROPOSITION XT. 301. Theorem. — Two parallelograms having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are equal. DEM.— Let AC and EC be two parallelograms, with AD = EH, AB = EF, and A = E ; then are...
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 270 pages
...584, Theorem.—On the same or equal spheres, two spherical triangles having two sides and theincluded angle of the one equal to two sides and the included angle of the other, each to each, are equal, or symmetrical and equivalent. FIG. 337. Fio. &38. DEM.—Let ABC and A'B'C', Fig. 337,...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...produced, the exterior angle is equal to the sum of the two interior and opposite. THEOREM VIII. 40. 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 two triangles are equal in...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...produced, the exterior angle is equal to the sum of the two interior and opposite. THEOREM VIII. 40, 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 two triangles are equal in...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DE F1, having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are themselves equal (Theo. IV. Bk. I.) But the triangle AGH is similar to ABC; therefore DEF is also...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1873 - 132 pages
...angle DBC = C DB ; therefore the whole angle ABC=.ADC; therefore the triangles ABC and ADC, having two sides and the included angle of the one equal to two sides and the included angle of the other, are equal (40). 49. Scholium. In equal triangles the equal angles are opposite the equal...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...equal to the angle D (Post. 7) ; make AG equal to DE, and draw GC. Tn"en will the triangles AGC and DEF have two sides and the included angle of the one equal...and the included angle of the other, each to each; consequently, GC is equal to EF (PV). Now, the point G may be without the triangle ABC, it may be on...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DE F. Laving two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are themselves equal (Theo. IV. Bk. I.) But the triangle AGH is similar to ABC; therefore DEF is also...
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