1. Recalling geometrical lines

In our previous classes, we must have learnt about geometrical lines and their types.

 

Let us recall those lines in this section and reset our memories.

 

Lines are everywhere. It is in the construction of buildings, roads, railway tracks, and so on.

 

Let us now look at different types of lines.

1. Intersecting lines: When two lines cross each other, then they are called intersecting lines. The point at which the two lines intersect is the point of intersection.

 

Consider the two lines \(a_1\) and \(a_2\). They meet each other at the point \(P\). Thus \(P\) becomes the point of intersection.

 

 

  

2. Concurrent lines: When three or more lines meet each other at the same point, then they are called concurrent lines. The point at which the lines meet is the point of concurrency.

 

In the figure given below, the three lines \(a_1\), \(a_2\), and \(a_3\) meet each other at the same point \(P\). Thus, \(a_1\), \(a_2\), and \(a_3\) become the concurrent lines, and the point \(P\) becomes the point of concurrency.

 

 

  

3. Perpendicular lines: When two lines cut each other at \(90\) degrees, they are called perpendicular lines.

 

The lines \(a_1\) and \(a_2\) meet each other at \(90\) degrees. Thus, they become perpendicular lines.

 

We can also denote the perpendicular lines as \(a_1 \perp a_2\).

 

 

  

4. Parallel lines: When two or more lines do not meet each other, they are called parallel lines.

 

In the figure given below, the lines \(a_1\) and \(a_2\) do not meet at all. These lines are called parallel lines.

 

Parallel lines can also be denoted as \(a_1 \parallel a_2\).