| Edward Olney - Geometry - 1872 - 239 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... | |
| Edward Olney - Geometry - 1872 - 239 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... | |
| Edward Olney - Geometry - 1872 - 327 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,... | |
| William Frothingham Bradbury - Geometry - 1872 - 110 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... | |
| William Frothingham Bradbury - Geometry - 1872 - 238 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... | |
| Benjamin Greenleaf - Geometry - 1873 - 176 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... | |
| William Frothingham Bradbury - Geometry - 1873 - 110 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... | |
| Geometry - 1874 - 455 pages
...equal to the angle D (Post. 7) ; make AG equal to DE, and draw GC. Tn"en 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... | |
| Benjamin Greenleaf - Geometry - 1874 - 176 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... | |
| 1875
...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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