 | George Bruce Halsted - Geometry - 1885 - 389 pages
...angle.) And for the same reason, in A CFB the sum 44 THEOREM XVIII. 159. If two triangles have two sides of the one equal respectively to two sides of the...will be greater than the third side of the second. HYPOTHESIS. ABC and DEF are two triangles, in which AB = DE, BC = EF, £ ABC > £ DEF. CONCLUSION.... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...coincides with ABC. TWO-DIMENSIONAL SPHERICS. THEOREM VI. 689. If two spherical triangles have two sides of the one equal respectively to two sides of the...will be greater than the third side of the second. HYPOTHESIS. AB = DE, and AC = EF, but £BAC> £ EDF. CONCLUSION. BC > EF. PROOF. When AB coincides... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...angle of an equiangular triangle? 31 PROPOSITION XXIII. THEOREM. 86. If two triangles have two sides of one equal respectively to two sides of the other,...first greater than the included angle of the second, the third side of the first is greater than the third side of the second. In the triangles ABC and... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...ED \ 46 PLANE GEOMETRY. — BOOK I. PROPOSITION XXVII. THEOREM. 152. If two triangles have two sides of the one equal respectively to two sides of the...will be greater than the third side of the second. ~'-.c\ A In the triangles ABC and ABE, let AB = AB, BC=BE; but /.ABC greater than ^AEE. To prove AC... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...the middle point of the third side. Proposition 29. Theorem. 119. If tii-o Iriunifle* have two sides of the one equal respectively to two sides of the, other, but the included angle in the first triangle greater than the included angle in the second, then the third side of the first... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...Z EFH > Z EHF. .-. EH>EF. Proposition 3O. Theorem. 120. Conversely, if two triangles have two sides of the one equal respectively to two sides of the other, but the third side of the first triangle greater than the third side of the second, then the included angle... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 204 pages
...or, a method similar to that in 122 may be employed. 123 (a). If two triangles have the two sides of one equal respectively to two sides of the other, but the included angles unequal, then the third side of that triangle having the greater included angle is longer than... | |
 | George Albert Wentworth - Geometry, Plane - 1892 - 266 pages
...152. If two triangles have two sides of the one equal respectively to two sides of the other, bufthe included angle of the first greater than the included...will be greater than the third side of the second. In the triangles ABC and ABE, let AB = AB, BC=BE; but £ABC greater than £ABE. To prove AC> AE. Proof.... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...equal respectively to two sides of the oiher, but the included angle of the first greater than thc included angle of the second, then the third side...will be greater than the third side of the second. ln the triangles ABC and ABE, let AB = AB, BC= BE ; but £ABC greater than £ABE. To prove AC>AE. Proof.... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...upon it. PRINCETON COLLEGE, June, 1891. 1. Prove that if two triangles have two sides of the one equal to two sides of the other, but the included angle...will be greater than the third side of the second. Also prove the converse. 2. Prove that a straight line perpendicular to a diameter of a circle at its... | |
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... greater than the included angle of the second, then the third side of the first is greater than the third side of the second. 
