 | 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
...that angle ACD equals angle A, prove (1)that CD bisects the hypotenuse AB, and (2) that if angle ACD is not equal to A, CD does not bisect the hypotenuse....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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If two angles of a triangle are unequal, the sides opposite them are unequal and the greater side is opposite the greater angle. 
