Here are the five postulates:
- Each pair of points can be joined by one and only one straight line segment.
- Any straight line segment can be indefinitely extended in either direction.
- There is exactly one circle of any given radius with any given center.
- All right angles are congruent to one another.
- 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 extended indefinitely, meet on that side on which the angles are less than two right angles.
These to me sounds more like something that shouldn't require proving... does it?
Why is it important to stress things that are obvious? For example, what other answers can you get when extending a line segment other than it can be extended indefinitely in either direction?
Similarly, what space can allow two circle of the same radius and center to be not the same?
Saying all right angles are congruent ... isn't that the same as saying all 64.506 degree angles are congruent? Isn't it ANY angle are congruent if they are the same degrees measures from the same reference point (say x-axis)?
Why do we need the 5th postulate?