 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...  A Treatise on Special Or Elementary Geometry - Page 128by Edward Olney - 1882 - 239 pagesFull view - About this book
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...< D. Hence, since A is neither > D nor < D, A must •— D. Then in the two triangles, we have two sides and the included angle of the one equal to two sides and the included angle of the other; hence, they are equal in all their parts; hence, B = E and C =: F. Therefore, etc. Scholium.—In... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...in AD or AD produced, as E'H'. Now, the two triangles AE'B and DH'C are equal, since they have two sides and the included angle of the one equal to two sides and the included angle of the other; viz., AB = DC, being opposite sides of a parallelogram ; and for a like reason BE' =... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...triangles be 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, AB : DE = AC : DF. Therefore,... | |
 | William John M'Clelland - 1885 - 182 pages
...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 to two...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... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...be greater nor less than D : hence, it must be equal to it. The two triangles have, therefore, two sides and the included angle of the one equal to two...and the included angle of the other, each to each ; and, consequently, they are equal in all respects (PV) ; which was to be proved. Scholium. In triangles,... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...perpendicular to each other, and bisect the angles of the rhombus. PROPOSITION XLII. THEOREM. 185. Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal. J7 CC! C' A! In the parallelograms... | |
 | 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.... | |
 | 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.... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...parallelograms may be made to coincide, and are equal. Conclusion : ABCK and EFSH being, etc. Corollary I. Parallelograms having two sides and the included angle...included angle of the other, each to each, are equal. PROPOSITION XVIII. 21O. Theorem : t parallelogram is divided by either of its diameters into two equal... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...lines, and it is, therefore, the required triangle. PROPOSITION I. Theorem : // two triangles have two sides and the included angle of the one equal to two...and the included angle of the other, each to each, they are equal in all their parts. Statement : Let the two triangles 123 and 456 have the side / 2... | |
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