 | Edward Olney - Geometry - 1872 - 562 pages
...bringing together the two greatest sides. Fia. 210. PROPOSITION X. 295. Theorem. — If two triangles hare two sides of the one respectively equal to two sides...third sides are unequal, and the greater third side Iclongs to the triangle having the greater included angle. ELEMENTARY PLANE GEOMETRY. DEM.— Let ACB... | |
 | Eli Todd Tappan - Geometry - 1873 - 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... | |
 | 1873 - 192 pages
...Prove that the area of a circle of which r is the radius is equal to if t 2 . VII. 1. Prove that if two triangles have two sides of the one respectively equal to two sides of the other, while the included angles are unequal, the third sides will be unequal, and the greater third side... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...- = GF, BG+GC>BF. But, BG + GC •= BC, and BF = EF, BC>EF. 74. Proposition XXX.— Theorem. If two triangles have two sides of the one respectively equal to two sides of the other and the third side of the one greater than the third side of the otlier, tlie angle opposite the greater third... | |
 | Robert Potts - Geometry - 1876 - 446 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... | |
 | Richard Wormell - 1876 - 268 pages
...a similar set. It may, for instance, be used to prove the converse of (6), namely : — " When two triangles have two sides of the one respectively equal to two sides of the other, but the base of one greater than the base of the other, the vertical angle which is opposite the greater... | |
 | Robert Fowler Leighton - 1877 - 372 pages
...GEOMETRY. 1. DEFINE a plane, a parallelogram, a trapezoid, a tangent to a circle. 2. Prove that when two triangles have two sides of the one respectively equal to two sides of the other and the included angle of the first greater than the included angle of the second, the third side of the first is greater... | |
 | James McDowell - 1878 - 310 pages
...angle. CoR 19 25. Given the three bisectors of the sides of a triangle ; construct it. DBF 20 26. If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, they are equal in area 20 27. If squares be described on the sides of... | |
 | Eli Todd Tappan - Geometry - 1868 - 454 pages
...parts alone arc never enough to determine a triangle. 98 UNEQUAL TRIANGLES. 293. Theorem. — When two triangles have two sides of the one respectively equal...other, and the included angles unequal, the third side in that triangle which has the greater angle, is greater than in the other. Let BCD and AEI be... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...the equal angles lie opposite the equal sides. ELEMENTS OF PLANE GEOMETRY. THEOREM XXVII. 89. If two triangles have two sides of the one respectively equal...third sides are unequal, and the greater third side is in the triangle having the greater included angle. In the As ABC and DEF, let AC = DF, CB = FE,... | |
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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. 
