RD Sharma Class 9 Solutions Chapter 8 - Lines and Angles (Ex 8.4) Exercise 8.4

Lines and angles are the basic terms that set up the basic foundation for geometry as a whole.

A line is defined as a row of closely placed dots that extends in two opposite directions in an infinite manner. The line has only one single dimension which is its length. The mathematician Euclid defined line as a breadthless length. In a standard cartesian plane, a line can be denoted by the linear equation which is of the form ax + by = c. 

Rays can be defined as the lines with one end as its starting point and the other end extending upto infinity. Rays only extend in one single direction without any end. When two rays are joined end to end, an angle is formed. 

An angle is defined as something created when two rays meet at a particular endpoint. Angles are usually measured in degrees using a device called a protractor. All geometric shapes have lines and angles in them. An angle can have any value between 0 degrees to 360 degrees. 

Types of Lines

Depending upon their properties, lines can be of different types: 

Horizontal line: These are the types of lines which when in a cartesian plane are parallel to the x-axis and perpendicular to the y-axis. In other words, it makes 0 degrees angle with the x-axis and 90 degrees with the y-axis. 

Vertical line: These are the types of lines which when in a cartesian plane are parallel to the y-axis and perpendicular to the x-axis. In other words, it makes 0 degrees angle with the y-axis and 90 degrees with the x-axis. 

Parallel lines: A pair of lines which are moving alongside with a constant distance between each other at any given point are called parallel lines. They make a 0 degree angle. 

Perpendicular lines: When two lines touch each other at an angle of 90 degrees, they are known as perpendicular lines. 

Transversal lines: When a common line intersects two lines at two different respective points, the whole system is called transversal lines. 

Types of Angles

Angles are of different types. They can be divided based on their measurements. There are six types of angles based on measurements,they are:

Acute angle: It is an angle in which the measurement of an angle is less than 90 degrees.

Obtuse angle: It is an angle in which the measurement of an angle is greater than 90 degrees and less than 180 degrees.

Right angle: It is an angle in which the measurement is equal to 90 degrees.

Straight Angle: It is an angle in which the measurement is equal to 180 degrees.

Reflex angle: It is an angle in which the measurement of an angle is greater than 180 degrees and less than 360 degrees.

Complete angle: It is an angle in which the measurement is 360 degrees.