Proposition 1.28 states:
If a straight line falling on two straight lines makes the sum of the interior angles on the same side equal to two right angles, then the straight lines are parallel to one another.
Euclid has given a somewhat long proof of this but I believe it is a direct consequence of his fifth postulate:
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.
What am I missing?