 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.  Elements of Plane Geometry - Page 48by Thomas Hunter - 1878 - 132 pagesFull view - About this book
 | Charles Davies - Geometry - 1872 - 464 pages
...(A. 8). Hence, CB must be the prolongation of AC ; which was to be proved. PROPOSITION V. THEOREM. If two triangles have two sides and the included angle...and the included angle of the other, each to each, the triangles will be equal in all their parts. to DE, AC to DF, and the angle A to the angle D: then... | |
 | Edward Olney - Geometry - 1872 - 566 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 - 472 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 - 1872 - 270 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 - 268 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 - 124 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 - 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 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 - 138 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... | |
 | Adrien Marie Legendre - Geometry - 1874 - 512 pages
...(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...and the included angle of the other, each to each, the triangles will be equal in att their parts. In the triangles ABC and DEF, let AB be equal to DE,... | |
 | 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... | |
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