NCERT Class 6 Maths Basic Geometrical Ideas

Basic Geometrical Ideas

4.1 Introduction

Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints. Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas. Even today geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, cloth designing etc. You observe and use different objects like boxes, tables, books, the tiffin box you carry to your school for lunch, the ball with which you play and so on. All such objects have different shapes. The ruler which you use, the pencil with which you write are straight. The pictures of a bangle, the one rupee coin or a ball appear round. Here, you will learn some interesting facts that will help you know more about the shapes around you.

4.2 Points

By a sharp tip of the pencil, mark a dot on the paper. Sharper the tip, thinner will be the dot. This almost invisible tiny dot will give you an idea of a point. A point determines a location.

These are some models for a point : If you mark three points on a paper, you would be required to distinguish them. For this they are denoted by a single capital letter like A,B,C. These points will be read as point A, point B and point C. Of course, the dots have to be invisibly thin.

4.3 A Line Segment

Fold a piece of paper and unfold it. Do you see a fold? This gives the idea of a line segment. It has two end points A and B. Take a thin thread. Hold its two ends and stretch it without a slack. It represents a line segment. The ends held by hands are the end points of the line segment.

The following are some models for a line segment :

Try to find more examples for line segments from your surroundings. Mark any two points A and B on a sheet of paper. Try to connect A to B by all possible routes. 

What is the shortest route from A to B?

This shortest join of point A to B (including A and B) shown here is a line segment. It is denoted by AB or BA . The points A and B are called the end points of the segment.

4.4 A Line

Imagine that the line segment from A to B (i.e. AB ) is extended beyond A in one direction and beyond B in the other direction without any end (see figure). You now get a model for a line.

Do you think you can draw a complete picture of a line? No. (Why?)

A line through two points A and B is written as AB It extends indefinitely in both directions. So it contains a countless number of points. (Think about this).

Two points are enough to fix a line. We say ‘two points determine a line’. 

The adjacent diagram (Fig 4.3) is that of a line PQ written as PQ Sometimes a line is denoted by a letter like l, m.

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