Introduction

Since, we already are aware of the basic definitions and concepts regarding lines and angles from the earlier classes, let's move on to some more important properties.

Here, we will be looking at some tried, tested and proven properties of the angles formed when two lines intersect each other, properties of the angles formed when a line intersects two or more parallel lines at distinct points.

These axioms are important to be understood, as these very concepts further on help us in understanding our world better.

For example: force application along with its direction on a given object, ray diagrams of concave and convex lens/mirrors etc.

From the simplest to the most complex ones, all arrangements existing in our world are made up of lines and angles.

In this chapter, you 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 you will use these properties to prove some statements using deductive reasoning.

In science, you 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 the other medium, you use the properties of intersecting lines and parallel lines.

When two or more forces act on a body, you 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, you 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, one needs 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, you will be using these properties of lines and angles to deduce more and more useful properties.

Lighthouse

Ray diagrams give us a representation of the behaviour of light rays when coinciding with objects.

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