 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...it is greater than either of them. THEOREM X. 80. If two triangles have two sides and the inchided angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects. In the triangles ABC, DEF, let the side AB equal DE, AC equal... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...9) Or, because QU= QW (I.), TQ+QU= TU> TW. 6. Comparing with (4), TU> TV. QED 45 THEOREM XIX. 108. If two triangles .have two sides and the included angle of the one equal to two sides and the included angle of the other, they are identically equal. Hypothesis. ABC&n&MNP,... | |
 | Richard Wormell - Geometry, Plane - 1883 - 210 pages
...those of the second ; and let LA = L E. Draw the diagonals BD, FH. The triangles ABD, EFH , having two sides and the included angle of the one respectively equal to two sides and the included angle of the other, are equal, and BD = F H. Then triangles B С D, FGH, having three sides of one respectively... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...and ED take the direction BC; then EF will take the direction BH, and ABH = ABC + DEF. THEOREM IV. 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 triangles will be equal in... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...+ DB < AC + CB. NOTE. — Have pupils give demonstration, prolonging BD instead of AD. THEOREM XII. If two triangles have two sides and the included angle...respectively, equal to two sides and the included, angle of the other, they are equal throughout. The triangles ACB and DFE have AC, the ang. A, and AB respectively... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...pupils give demonstration, prolonging BD instead of AD. THEOREM XII. If two triangles have two aides and the included angle of the one, respectively, equal to two sides and the included angle of the other, they are equal throughout. Conceive the triangle ACB to move to the right till AB coincides... | |
 | William John M'Clelland - 1885 - 182 pages
...three given ares (any two of which being supposed greater than the third}. (Cf. Euc. I. xxii.) (7). 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 triangles are equal in every... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...other, by Proposition IX., and B is equal to B'. The triangles ABC and A' B'C' have now been proved to have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, and are equal, by Proposition VI. PROPOSITION XI.—THEOREM. 27. If two angles of a triangle... | |
 | Euclid - Geometry - 1890 - 442 pages
...side BC = side YZ, side CA = side ZX ; and, finally, area ABC = area XYZ. Proposition 4. THEOREM — If two triangles have two sides and the included angle...respectively equal to two sides and the included angle of the other, then the triangles are identically equal, and of the angles those are equal which are... | |
 | Thomas J. Foster - Coal mines and mining - 1891 - 444 pages
...opposite or vertical angles are equal. 4. If two angles have their sides parallel they are equal. 5. If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, they are equal in all their parts. If two triangles... | |
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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. 
