 | 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...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... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...and the 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 - 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... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...join A' and C' by the arc of a great circle : then, because the triangles IS AC and B'A'C' have two sides and the included angle of the one, equal to...and the included angle of the other, each to each, the remaining parts will be equal, eacl to each • that is, A'C' = AC, and the angle A' equal to tLo... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...by construction, AG is equal to DE; hence AH is equal to D F. Therefore the two triangles AGH, DEF, having two sides and the included angle of the one...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... | |
 | B. Marks - 1875 - 176 pages
...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 equal to...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... | |
 | Edward Olney - Geometry - 1876 - 354 pages
...triangles minus the third. PROPOSITION XVIII. 584. Theorem,—On the same or equal spheres, two spherical triangles having two sides and the included angle...and the included angle of the other, each to each, are equal, or symmetrical and equivalent. FIG. 337. FIG. 388. DEM.—Let ABC and A'B'C', Fig. 337,... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...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...and the included angle of the other, each to each; hence, they are equal in all their parts; therefore, the angle EA'D is equal to EAD, and the side DA'... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...draw the arc DA'. The right• angled triangles AED and A 'ED, have two sides and the included atigle 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 equal to EAD, and the side... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...form of quadrilateral.] PROPOSITION XV. 301, Theorem,—Two parallelograms having two sides and tin Included angle of the one equal to two sides 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 they... | |
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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... 
