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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 Trigonometry - Page 24
by Adrien Marie Legendre - 1852 - 432 pages
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Marks' First Lessons in Geometry: In Two Parts : Objectively Presented and ...

Bernard Marks - Geometry - 1871 - 172 pages
...the angle ADC. Therefore the angle AB c is equal to the angle ADC. Then the two triangles AB c, AD c, have two sides, and the included angle of the one...and the included angle of the other, each to each, and are equal in all their parts ; that is, the three angles of the one are equal to the three angles...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...because AB is equal to CD, and BC is common to the two triangles <VBC BCD, the two triangles ABC, BCD have two sides and the included angle of the one, equal to two sides and the in. duiled angle of the other ; therefore, the side AC is equa\ to BD (Prop. VI.), and the angle ACB...
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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, 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 - 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

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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