NCERT Book Class 6 Maths Understanding Elementary Shapes

Understanding Elementary Shapes

5.1 Introduction

All the shapes we see around us are formed using curves or lines. We can see corners, edges, planes, open curves and closed curves in our surroundings. We organise them into line segments, angles, triangles, polygons and circles. We find that they have different sizes and measures. Let us now try to develop tools to compare their sizes.

5.2 Measuring Line Segments

We have drawn and seen so many line segments. A triangle is made of three, a quadrilateral of four line segments. A line segment is a fixed portion of a line. This makes it possible to measure a line segment. This measure of each line segment is a unique number called its “length”. We use this idea to compare line segments.

To compare any two line segments, we find a relation between their lengths. This can be done in several ways.

(i) Comparison by observation:

By just looking at them can you tell which one is longer?

You can see that AB is longer.

But you cannot always be sure about your usual judgment.

For example, look at the adjoining segments :

The difference in lengths between these two may not be obvious. This makes other ways of comparing necessary.

In this adjacent figure, AB and PQ have the same lengths. This is not quite obvious.

So, we need better methods of comparing line segments.

(ii) Comparison by Tracing

To compare AB and CD, we use a tracing paper, trace CD and place the traced segment on AB.

Can you decide now which one among AB and CD is longer? 

The method depends upon the accuracy in tracing the line segment. Moreover, if you want to compare with another length, you have to trace another line segment. This is difficult and you cannot trace the lengths everytime you want to compare them.

(iii) Comparison using Ruler and a Divider

Have you seen or can you recognise all the instruments in your instrument box? Among other things, you have a ruler and a divider.

Note how the ruler is marked along one of its edges. It is divided into 15 parts. Each of these 15 parts is of length 1cm.

Each centimetre is divided into 10subparts.

Each subpart of the division of a cm is 1mm.

How many millimetres make one centimetre? Since 1cm = 10 mm, how will we write 2 cm? 3mm? What do we mean by 7.7 cm?

Place the zero mark of the ruler at A. Read the mark against B. This gives the length of AB. Suppose the length is 5.8 cm, we may write, Length AB = 5.8 cm or more simply as AB = 5.8 cm.

There is room for errors even in this procedure. The thickness of the ruler may cause difficulties in reading off the marks on it.

EXERCISE 5.1

1. What is the disadvantage in comparing line segments by mere observation?

2. Why is it better to use a divider than a ruler, while measuring the length of a line segment?

3. Draw any line segment, say AB. Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB? 

[Note : If A,B,C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B.]

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