I was going through Euclid's elements when I noticed Book I, Proposition 17, which states that:
In any triangle the sum of any two angles is less than two right angles.
And also Euclid's 5th postulate which states that:
If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
So suppose I take two lines AB and CD which would intersect if produced indefinitely and pass a transversal through it as showing in the figure below
Then I would say that AOC is a triangle, where O is the intersection point of the two lines. So can't I just say that by Book I, Proposition 17, 5th Postulate is proven, and therefore technically not a postulate? But it doesn't seem to be the case. Why is it so?