 | William Frothingham Bradbury - 1872 - 124 σελίδες
...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... | |
 | William Frothingham Bradbury - 1872 - 262 σελίδες
...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... | |
 | Edward Olney - 1872 - 270 σελίδες
...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... | |
 | William Frothingham Bradbury - 1873 - 132 σελίδες
...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... | |
 | Benjamin Greenleaf - 1873 - 202 σελίδες
...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 sides and the included angle of the other, each to each, are themselves equal (Theo. IV. Bk. I.) But the triangle AGH is similar... | |
 | Adrien Marie Legendre - 1874 - 500 σελίδες
...(A. 8). Hence, CB must be the prolongation of AC ; which was to be proved. PROPOSITION Y. THEOREM. If two triangles have two sides and the included angle...the one equal to two sides and the included angle of the other, each to each, the triangles will be equal in att their parts. In the triangles ABC and... | |
 | Benjamin Greenleaf - 1874 - 206 σελίδες
...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 sides and the included angle of the other, each to each, are themselves equal (Theo. IV. Bk. I.) But the triangle AGH is similar... | |
 | B. Marks - 1875 - 176 σελίδες
...What do you think of the areas of the triangles ? a d I cef DEMONSTRATION. We wish to prove, that, // two triangles have two sides, and the included angle...the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects. Let the triangles abc and... | |
 | William Guy Peck - 1876 - 376 σελίδες
...meet at C'. Lay off EA' equal to EA, and draw the arc DA'. The rightangled triangles AED and A'ED, have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each; hence, they are equal in all their parts; therefore, the angle EA'D is... | |
 | Elias Loomis - 1877 - 458 σελίδες
...together be equal to the sum of all the angles BAC, CAD, etc., formed about A. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included...the one equal to two sides and the included angle of the other, each to •each, the two triangles will be equal, their third sides will be equal, and... | |
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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. 
