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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 in all their parts." Axiom 1. "Things which are equal to the same thing, are equal... "
Manual of Geometry and Conic Sections: With Applications to Trigonometry and ... - Page 273
by William Guy Peck - 1876 - 366 pages
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The Eclectic School Geometry: A Revision of Evan's School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...similar. Take AG equal to DE, and AH to DF; also, join GH. Then the triangles AGH, DEF, having two sides and the included angle of the one equal to two sides and the included angle of the other, are equal throughout (Theo. XII, Book I). Now, by hypothesis, Hence, it follows that...
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A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Part 1

William John M'Clelland - 1885 - 182 pages
...(any two of which being supposed greater than the third}. (Cf. Euc. I. xxii.) (7). If two triangles have two sides and the included angle of the one equal...and the included angle of the other, each to each, the triangles are equal in every respect. For, since two sides of given length intersecting at a given...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...CAG equal to the angle D (Post. 7) ; make AG equal to DE, and draw GC. Then 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...
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...is less. Proposition XXVI. A Theorem. 63. If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal. Proposition XXVII. A Theorem....
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 80 pages
...is less. Proposition XXVI. A Theorem. 63. If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal. Proposition XXVII. A Theorem....
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...SYNOPSIS* SECTION I.— EQUAL TRIANGLES. 105. i. DEFINITIONS. 2. PROPOSITIONS. PROP. I. If two triangles have two sides and the included angle of the one equal...and the included angle of the other, each to each, they are equal in all their parts. PROP. II. If two triangles have two angles and the included side...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...EQUAL TRIANGLES. 105. i. DEFINITIONS. 2. PROPOSITIONS. PROP. I. If two triangles have two sides an'l the included angle of the one equal to two sides and the included angle of the other, each to each, they are equal in all their parts. PROP. II. If two triangles have two angles and the included side...
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The Colliery Engineer Pocket-book of Principles Rules, Formulæ, and Tables ...

Thomas J. Foster - Coal mines and mining - 1891 - 444 pages
...vertical angles are equal. 4. If two angles have their sides parallel they are equal. 5. If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, they are equal in all their parts. If two triangles have two angles and the included...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 426 pages
...lines, and it is, therefore, the required triangle. PROPOSITION I. 122. Theorem : // two triangles have two sides and the included angle of the one equal to two sides and the included anyle of the other, each to each, they are equal in all their parts. Statement : Let the two triangles...
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The Elements of Physics

Henry Smith Carhart, Horatio Nelson Chute - Physics - 1892 - 400 pages
...and A'KB, we have the angles at K equal, and hence right angles, and AK = A'K, since the triangles have two sides, and the included angle of the one equal to the corresponding parts of the other. D N Fig. 232. dicular to MN, and A' is as far back of MN as A...
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