In any triangle the greater angle is subtended by the greater side.
Let ABC be a triangle having the angle ABC greater than the angle BCA; I say that the side AC is also greater than the side AB. For, if not, AC is either equal to AB or less. Now AC is not equal to AB; for then the angle ABC would also have been equal to the angle ACB; [I. 5] but it is not;
Q. E. D.