NCERT Class 9 Mathematics Textbook for Blind Students made Screen Readable by Professor T K Bansal.

In Chapter 5, we studied that a minimum of two points are required to draw a unique line. We also studied some axioms, and with the help of these axioms, we proved some other statements. In this chapter, we will study the properties of the angles formed when two lines intersect each other, and also the properties of the angles formed when a line intersects two or more parallel lines at distinct points. Further we will use these properties to prove some statements using deductive reasoning (see Appendix 1). We have already verified these statements through some activities in the earlier classes.

In our daily life, we come across different types of angles formed between the edges of plane surfaces. For making a similar kind of model using the plane surfaces, we need to have a thorough knowledge of angles. For instance, suppose we want to make a model of a hut to keep in the school exhibition using bamboo sticks. Imagine how we would make it? We would keep some of the sticks parallel to each other, and some sticks would be kept slanted. Whenever an architect has to draw a plan for a multistoried building, she has to draw intersecting lines and parallel lines at different angles. Without the knowledge of the properties of these lines and angles, do you think she can draw the layout of the building?

In science, we study the properties of light by drawing the ray-diagrams. For example, to study the refraction property of light when it enters from one medium to another, we use the properties of intersecting lines and parallel lines.

When two or more forces act on a body, we draw the diagram in which forces are represented by directed line segments to study the net effect of the forces on the body. At that time, we need to know the relation between the angles when the rays (or line segments) are parallel to or intersect each other.

To find the height of a tower or to find the distance of a ship from the light house, we need to know the angle formed between the horizontal and the line of sight.

Plenty of other examples can be given where lines and angles are used. In the subsequent chapters of geometry, we will be using these properties of lines and angles to deduce more and more useful properties.

Let us first revise the terms and definitions related to lines and angles learnt in earlier classes.