 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...inequality between the sides AB, AC ; hence the triangle ABC is isosceles. (M THEOREM. f<{ 49. If either two angles of a triangle are unequal, the sides opposite them are also unequal, and the greater side is opposite the greater angle ; and conversely, if the sides ^-e... | |
 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...equal, the sides opposite those angles are equal, ie the triangle will be isosceles. 32. THEOREM. If two angles of a triangle are unequal, the sides opposite them are unequal, and the greater side lies opposite the greater angle. Let ABC represent the triangle, the angles of which at A and B are... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...distant from the extremities of that line. If two angles of a triangle are unequal the sides opposite to them are unequal and the greater side is opposite the greater angle. The three bisectors of the angles of a triangle meet in a point. NOTE. — The pseudo-sphere, page... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...distant from the extremities of that line. If two angles of a triangle are unequal the sides opposite to them are unequal and the greater side is opposite the greater angle. The three bisectors of the angles of a triangle meet in a point. NOTE. — The pseudo-sphere, page... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...opposite to them are unequal, the greater angle being opposite the greater side; and conversely, if two angles of a triangle are unequal, the sides opposite them are unequal, the greater side lying opposite the greater angle. F CE Let ABC be a A having AB>BC. To Prove ZOZ^l.... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...etc. PROPOSITION XXIV. — THEOREM. // two angles of a triangle are unequal, the sides opposite to them are unequal, and the greater side is opposite the greater angle. Given. — Let ABC be a triangle having the angle ABC greater than CAB. To Prove. — Then we are to... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...triangle is isosceles. 76. Corollary. An equiangular triangle is also equilateral. 77. Theorem XXVIII. If two angles of a triangle are unequal, the sides opposite them are unequal, the greater side being opposite the greater angle. 78. Corollary. The hypotenuse is the greatest side... | |
 | George Clinton Shutts - 1905 - 260 pages
...B is equal to angle C. To prove that the side AC is equal to the side A B. Suggestion 1. Drop a _L from A to BC, as A M. 2. Compare As AMB and AM C....1. Draw CM to represent a line making Z. o equal to /L B. Is this possible ? 2. Compare BM and C M. Give auth. j. Compare CM + MA with CA, BA with C A.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...^ftc = Z a; (?) (55). Again, Z ^CB > Z a; (?) (Ax. 5). .-. Z ^CB > ZB (Ax. 11). QED 123. THEOREM. If two angles of a triangle are unequal, the sides opposite them are unequal and the greater angle is subtended by the greater side. Given: A.4BC; To Prove: AB > AC. Proof: In Z ACB, suppose Z... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...Z ^KC = Z z (?) (55). Again, Z ^CB > Z z (?) (Ax. 5). ... Z ACB > ZB (Ax. 11). QED 123. THEOREM. If two angles of a triangle are unequal, the sides opposite them are unequal and the greater angle is subtended by the greater side. Given: AABC; ZACB>^.E To Prove: AB > AC. / XR Proof : In Z... | |
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Theorem. // two angles of a triangle are unequal, the sides opposite them are unequal, and the greater side is opposite the greater angle. 
