Given a point *l *and a point P. If P is an element of *l*,

then we say that P lies on *l*, or

P is incident on *l*, or *l* passes through P.

Now we can try to find answers to the following questions on the basis of our experience.

- Given a point P, is there a line that passes through P? how many such lines are there?
- Given two distinct points A and B, is there a line that passes through both a and B? How many such lines are there?
- Given a line
*l*, is there a point that lies on it? How many such points are there? - Given two distinct lines
*l*and*m*, is there a point that lies on both*l*and*m*? how many such points are there?

Based on the results of the above questions we can arrive at the following conclusions. These conclusions have to be taken as axioms.

**Incidence Axiom 1:** A line contains infinitely many points.

**Incidence Axiom 2:** Through a given point, there pass infinitely many lines.

**Incidence Axiom 3:** Given two distinct points A and B, there is one and only one line that contains both the points.

According to the third axiom, any two distinct points of the plane determine a line uniquely and completely.

**Definition:** Three or more than three points are said to be collinear, if there is a line which contains them all.

**Definition:** Three or more than three lines are said to be concurrent if there is a point which lies them all.

Labels: Geometry