01 · EUCLID'S 5 POSTULATES
The Five Geometric Postulates
5 POSTULATES
Euclid's Postulates Statement
1. Postulate 1: A straight line may be drawn from any one point to any other point.
2. Postulate 2: A terminated line can be produced indefinitely.
3. Postulate 3: A circle can be drawn with any centre and any radius.
4. Postulate 4: All right angles are equal to one another.
5. Postulate 5 (Parallel Postulate): If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles (180°), the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
02 · EQUIVALENT VERSIONS
Playfair's Axiom
For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l.