A line segment can be extended on its both sides endlessly to get a straight line.

1. Axioms and Theorems:

(i) There are three basic terms in geometry, namely "Point", "Line" and "Plane". It is not possible to define these three terms precisely. So, these are taken as undefined terms.

(ii) Axioms or postulates are the basic facts which are taken for granted without proof.

(iii) Theorems are statements which are proved through logical reasoning based on previously proved results and some axioms.

2. Euclid's Axioms:

(i) Axiom 1: A line contains infinitely many points.

(ii) Axiom 2: Through a given point there pass infinitely many lines.

(iii) Axiom 3: Given two points $A$ and $B,$ there is one and only one line that contains both the points. Given two points $A$ and $B,$ there is one and only one line that contains both the points.

3. Theorems based on Euclid's Axioms:

(i) Two distinct lines cannot have more than one point in common.

(ii) Two lines are intersecting if they have a common point. The common point is called the point of intersection.

(iii) Two lines are parallel if they do not have a common point i.e., they do not intersect.

4. Euclid’s Postulates:

(i) Postulate 1: A straight line may be drawn from anyone point to any other point.

(ii) Postulate 2: A terminated line can be produced indefinitely.

(iii) Postulate 3: A circle can be drawn with any centre and any radius.

(iv) Postulate 4: All right angles are equal to one another.

(v) Postulate 5: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

5. Two Equivalent Versions of Euclid’s Fifth Postulate:

(i) 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 $l$.

(ii) Two distinct intersecting lines cannot be parallel to the same line.