 | Benjamin Peirce - Geometry - 1837 - 216 pages
...case, and the equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Demonstration. In the two triangles ABC, D£JP(ng.31),... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...throughout, consequently they are equal. (Ax. 13.) Hence, universally, Any two triangles are every way equal, when two sides and the included angle of the one, are respectively equal to two sides and the included angle of the other. PROPOSITION VI. THEOREM. If two triangles ABC, DEF,... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...case, and the equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Proof. In the two triangles ABC, DEF, (fig. 31), let... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...construction, the side AB common, and the angle CAB equal to the angle CBA by hypothesis ; therefore two sides and the included angle of the one are respectively equal to two sides and the included angle of the other ; consequently the triangle DAB is equal to the triangle... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...construction, the side AB common, and the angle CAB equal to the angle CBA by hypothesis; therefore two sides and the included angle of the one are respectively equal to two sides and the included angle of the other ; consequently the triangle DAB is equal to the triangle... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...other so as to coincide in all their parts. PROPOSITION XX.— THEOREM. 76. Two triangles are equal when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. In the triangles ABC, DEF, let AB be equal to DE, BC... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...have seen in Props. 5, 6, and 7, that two triangles are equal in all their parts when — 1 st. Two sides and the included angle of the one are respectively equal to two sides and the included angle of the other ; or 2nd. When two angles and the included side of the... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...other so as to coincide in all their parts. PROPOSITION XX.—THEOREM. 76. Two triangles are equal when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. In the triangles ABC, DEF, let AB be equal to DE, BC... | |
 | Richard Wormell - 1876 - 268 pages
...rect. C R. Join IB, C M. Now AIAB = half rect. AQ, AC AM = half rect. AP; but AIAB = ACAM : For two sides and the included angle of the one are respectively equal to two sides and the included angle of the other ; . • . Rect. AQ = rect. A P. Similarly we may show... | |
 | Cornell University - 1880 - 868 pages
...are to each other as their bases. 3. Two triangles on the same sphere are either equal or symmetrical when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. 4. A frustum of any cone is equivalent to the sum of... | |
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If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other... 
