# Lines

Sub Topics

A line is a set of infinite points extending infinitely on both the sides in opposite directions. The length of a line is infinite, its height and width are zero. We can name the line by any two points on it.
The symbol of a line is shown by a double headed arrow $\leftrightarrow$, this symbol is written on top of the two letters used to label the line. A line can also be labeled using a single letter in small case, like l, m, n.

The figure denotes a line AB. It is written as $\overleftrightarrow{AB}$

The figure denotes a line a,b & m.

## Line Segment

A part or portion of a line with two end points is called a line segment.

A line segment is denoted by a line over the two points, $\overline{AB}$ and its length is denoted as AB

The above figure denotes a line segment. The points A and B are the end points of the line segment.
As the name suggests, segment means a piece of something. Here it means a part of a line. A line extends infinitely on both sides, a line segment is a part of this.

A line segment is a single dimensional geometrical figure, it has only length, no width or thickness.

## Types of Lines

Coplanar Lines:
Two or more lines lying in the same plane are called coplanar lines.

Non-Coplanar Lines:
Lines not lying in the same plane are called non-coplanar lines.

In the figure given above, lines l  and m  are coplanar lines lying in the same plane.
Lines n and p are non-coplanar lines, they do not lie in the same plane.

Intersecting lines: Two or more lines intersecting or meeting at one point are called intersecting lines. The point at which they meet is called the point of intersection. The point of intersection will lie on each of the lines.

The above figure shows the intersecting lines l and m, point P is the point of intersection.
Two or more lines having only one point in common are called intersecting lines.Some of the examples are, wire mesh, a cross.

Perpendicular Lines: Two lines intersecting forming a right angle are called perpendicular lines. The two lines are said to be perpendicular to each other.

In the above figure, lines p and q are perpendicular to each other and at R, the point of intersection the angle is a right angle
The symbol used to denote the perpendicular lines is $\perp$ , in the given figure given above, p $\perp$ q read as p is perpendicular to q
For example two adjacent sides of a photo frame, a telephone pole is perpendicular to the land on which it is erected.
Example: Consider three coplanar lines, a,b and c. If a is perpendicular b and c is perpendicular to b. Then which of the following statements are true
1.     Line a is line c (False)
2.     Line c  is perpendicular to a (True)
3.     Line c is 45° to line a (True)
4.     Line a is parallel to c (False)

Parallel lines:
Two co-planar lines that do not intersect at any point are called parallel lines. They are at a constant distance apart always. The symbol used to denote parallel lines is $\parallel$ . In the figure given below, the two lines l and m are parallel to each other.  l $\parallel$ m , which is read as l is parallel to m.

The rails of the railway tracks are the best example for parallel lines, they never intersect and the lines are always at a constant distance.