# NCERT Solutions for Class 9 Maths Chapter 6 – Lines and Angles PDF

## Free PDF of NCERT Solutions for Class 9 Maths Chapter 6 – Lines and Angles

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## Lines and Angles - Basic Terms

In geometry, lines and angles are the basic terms that set up the foundation for the subject. A line is defined as a row of closely spaced dots that extends infinitely in two directions. It has only one dimension, that is its length. A horizontal mark drawn on a piece of paper can be considered as an example of a line. An angle is defined as a figure created by two rays that meet at a common endpoint. They are measured in degrees, using a protractor. All geometry shapes have lines and angles in them. Let us learn more about the various types of lines and angles in this lesson.

## Definition of Lines and Angles

The concept of lines was introduced by the ancient mathematicians to represent straight objects that did not have any width or depth. While lines are simpler to understand, an angle is a shape that is formed by the intersection of two line segments, lines, or rays. When two rays intersect each other in the same plane, they form an angle.

## Lines

A line is a one-dimensional figure that extends in both directions infinitely without any width. It is made up of infinite number of points close to each other. Euclid denotes the line as a breadthless length. In a cartesian plane, it is denoted by the linear equation ax + by = c.

## Rays

Rays are the lines with one end as the start point and the other end going to infinity. They extend in one direction without ending. When two rays are joined end to end, they form an angle.They are represented as PQ→

## Line Segment

When a line has two endpoints, it is known as a line segment. The length of a line segment can be measured and it is written as ĀB

## Angles

When two rays intersect at a point, they form an angle. Angles are usually measured in degrees and denoted by ∘ (the degree symbol), which is a measure of rotation. An angle can have a value between 0∘ to 360∘ and it is denoted by the symbol ∠.Observe the following figure which shows ∠ ABC

### Types of Angles

Angles can be categorized into different types based on their measurements. Angles are generally of 6 types:

Acute angle: If the measure of an angle is less than 90∘ then it is known as an acute angle.

Obtuse angle: If the measure of an angle is greater than 90∘ but less than 180∘, then it is known as an obtuse angle.

Right angle: If the measure of an angle is exactly equal to 90∘ then it is known as a right angle

Straight angle: If the measure of an angle is 180∘ then it is known as a straight angle.

Reflex angle: If the measure of an angle is greater than 180∘ but less than 360∘, then it is known as a reflex angle.

Complete angle: If the measure of an angle is 360∘ then it is known as a complete angle.

## Properties of Lines and Angles

As we have seen that there are different kinds of lines and angles, each of them has different specific properties. However, there are some basic common properties of lines and angles that can be discussed.

### Properties of Lines

Lines can be defined as a set of an infinite number of points close to each other.
They extend infinitely in both directions.
They are one-dimensional and do not have any depth or thickness.

### Properties of Angles

An angle is a geometrical figure that is formed when two lines intersect each other in the same plane.
The lines that form an angle are termed as its arms (sides), and the point at which they form the angle is called its vertex.

### Tips on Lines and Angles

Here is a list of a few tips that should be remembered while studying lines and angles:

• All geometry shapes have angles and lines in them.
• A line is a one-dimensional figure, with no breadth, and that extends in both directions infinitely.
• These are the lines with one end as the start point and the other end going to infinity. These are used to form angles.
• Angles are formed when two rays intersect at a point.