 If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.  Elements of Plane Geometry - Page 44by Franklin Ibach - 1882 - 196 pagesFull view - About this book
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...a radius, describe a circumference in the plane MN, cutting CD at D. Then the triangles ACD and ACB have two sides of the one respectively equal to two sides of the other. But the third side AD is longer than the third side AB (530). Therefore, the angle ACD is greater than... | |
 | Robert Potts - 1865 - 528 pages
...then the angle of one triangle is supplemental to the other. Hence the following property : —If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. A distinction ought to be made between... | |
 | Euclides - 1865 - 402 pages
...I. 41. * ' The 4th, 8th, 24th, and,<25th propositions may be announced together thus : — ' if two triangles have two sides of the one respectively equal to two sides of the other, the remaining side of the one will be greater or less than, or equal to, the remaining side of the... | |
 | Robert Potts - 1868 - 434 pages
...then the angle of one triangle is supplemental to the other. Hence the following property : — If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. A distinction ought to be made between... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...angle A given, there are two triangles, ABC andABD. " ~5~ ~v UNEQUAL TRIANGLES. Theorem. — When two triangles have two sides of the one respectively equal to two sides of the other, and the induded angles unequal, the third side in that triangle which has the greater angle, is greater than... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...respectively equal to the three angles of another, while the triangles are unequal (fig. 79). When two triangles have two sides of the one respectively equal to two sides of the other, but the included angle of the one greater than the included angle of the other, the base of that which... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...radius, describe a circumference in the plane MN, cutting CD at D. N Then the triangles ACD and ACB have two sides of the one respectively equal to two sides of the other. But the third side AD is longer than the third side AB (530). Therefore, the angle ACD is greater than... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...angles in each, or opposite one of them, the triangles are equal in all respects. (§ &&b). 14. When two triangles have two sides of the one respectively equal to two sides of the other, but the angle contained by the two sides of the one greater than the angle contained by the two sides... | |
 | Charles Henry Winston, Richard M. Smith, D. Lee Powell, John Meredith Strother, H. H. Harris, John Patrick McGuire, Rodes Massie, William Fayette Fox, Harry Fishburne Estill (F.), Richard Ratcliffe Farr, John Lee Buchanan, George R. Pace - Education - 1882 - 580 pages
...abstraction. Now make the same statement in geometrical language. If two triangles have hvo sides of the one equal to two sides of the other and the included angles unequal, the third sides will be unequal also, and the greater third side will be in that triangle which has the greater included... | |
 | Edward Olney - 1872 - 270 pages
...secured by bringing together the two greatest sides. PROPOSITION X. Fio. 210. 295. Theorem.—If two triangles have two sides of the one respectively equal...third sides are unequal, and the greater third side belongs to the triangle having the greater included angle. third in the DEM.—Let ACB and DEF be two... | |
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