# Lines

Noble mathematicians introduced the concept of lines. The concept of geometry begins with a point. An infinite number of points with measurable or negligible distance between them combines together to form a line. A line can be a straight line or a curved line. Consider a rope. If the two ends of the rope are tied or held, it forms a straight line, whereas, if both the ends are not tied to anything then it forms a curved line.

Let us learn the basic definitions of point, line, ray, and line segment.

Point: An exact location that is represented by a dot is called a point. If three or more points lie on the same line, they are called collinear points;
Otherwise they are called non-collinear points. It is represented using any alphabet. For example, a point can be denoted by letters X, A, and so on.

Line: A straight set of points that extend in opposite directions without ending is called a line. A line is denoted by line AB or AB⃡.

Ray: A part of a line that has one endpoint and extends in one direction without ending is called a ray. A ray is denoted by ray AB or AB.

Line segment: A part of a line between two endpoints is called a line segment. A line segment is denoted by segment AB or AB. Ruler is the device used to measure the length of a line segment.

Example 1: Find the length of line segment AB.

Solution: From the image above, AC=AB+BC ⇒ AB=AC-BC
AB = 12 – 3 = 8 ft

## Types of Lines

Are all lines the same? There are different types of lines such as vertical lines, horizontal lines, parallel lines, perpendicular lines, and intersecting lines.

### Vertical lines and Horizontal lines

A line which runs from top to bottom is called a vertical line. A line which runs from left to right is called a horizontal line.

### Parallel lines

Lines that are always the same distance apart are called Parallel lines. These lines never meet and never cross. The symbol II is used to represent parallel lines. For example, the two lines AB and LM are represented as AB⃡ II LM⃡. It is read as line AB is parallel to line LM.

### Perpendicular lines

Perpendicular lines are those which meet or cross and form a right angle at their point of intersection. The symbol ⊥ is used to represent perpendicular lines. For example, the two lines QR and DE are represented as QR⃡ ⊥ DE⃡. It is read as line QR is perpendicular to line DE.

### Intersecting lines

Lines that meet or cross each other are called intersecting lines. There is no symbol used to represent intersecting lines. It is read as GH⃡ intersects EF⃡.

### Transversal Line

A line that connects two or more parallel lines is called a transversal line.

## Properties of Lines

Every type of a line has its own properties. The following are the various properties of the lines:

• The length of a line is infinite.
• The line is infinitely long in both directions.
• There are no endpoints on the lines.
• The line is a geometrical figure with only one dimension.
• There is no thickness to the line; it just has length.
• Intersecting lines will cross at only one point.
• The distance between parallel lines remains constant.
• A right-angle forms between the perpendicular lines.
• The line segment is the section of the line that connects the two points.
• There are an endless number of solutions to a line.
• The common perpendicular drawn between the two non-intersecting lines has the same length every time.
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Challenge yourself!

Identify the correct options that match the images.

Options: Line, Segment, Point, Ray

Surprising conclusion

Think and Reason

Suppose you have a ball tied to one end of a rope and you are rotating it by holding the other end. What will happen if you release the ball? Will the ball move in a curved line or a straight line?

How do you feel when you realize that a curved line is producing an invisible straight line? Fascinating isn’t it?

Similarly look at this picture. How is the rope being pulled to and fro in order to rotate the stick to cuddle the milk?
It is pulled in a straight line but yet produces circular or curved motion.

Is it not an irony to notice two opposite natured geometrical objects producing one another? There are ample examples like this where lines are a part and parcel of our daily lives, either in visible or invisible formats.

Take a cue from this reading and explore the splendid lines around and within you!

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