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Understanding Elementary Shapes

Consider two buildings A and B in the following figure.

Suppose you are standing on one side of the road and these two buildings are on the other side. Can you tell which building is taller?

Yes, you are right. Simply by looking at the buildings, you can say that the building on the left (i.e. building A) is taller. This is called the method of observation, where we look at two objects and say that which of them is taller or which is shorter.

Now, let us apply this concept of observation in geometry. You already know what a line segment is. Remember that the length of a line segment is the distance between its end points.

Now consider the line segments AB and CD drawn in the following figure.

Can you tell which line segment is longer?

Surely, you will not face any problem in answering this question. Simply by observing the two line segments, we can say that the length of CD is more than AB. We can also say the length of line segment AB is less than CD.

This method of comparison of lengths of line segments is the method of observation.

Now, in order to understand this concept in greater detail, let us take a look at the following video.

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Consider the line segments AB and CD drawn in the following figure.

Can you tell which line segment is longer?

Yes, simply by observing the line segments, we can say that the length of CD is more AB.

However, we cannot always tell which line segment is longer, merely by looking at them. For example: consider the following figure.

Can you say which line segment is longer – the blue one or the green one?

Here, you might be a little confused. Actually, in this figure, both line segments are of same length, even though, the green line segment seems longer than the blue one. This is an example of optical illusion.

So, is there any other way, by which we can compare the lengths of line segments without having such observation errors?

One such method is tracing. Let us now look at this method.

Consider the two line segments AB and CD given in the following figure.

Here, the line segments and seem to be of equal lengths. However, we cannot say this for sure. So, we can use the method of tracing in such cases, which is as follows.

• We start by tracing one line segment, say AB, using a tracing paper.

• We then place the traced line segment AB on the other line segment(CD) which needs to be compared.

This can be done as follows.

Now, we can say for sure that line segment AB is shorter than the line segment CD.

This technique of comparison of line segments is known as method of tracing.

Look at the line segments AB and CD shown in the following figure.

Can you say which of the two line segments is longer?

We know a method of comparing the lengths of the line segments i.e., the method of tracing. However, this technique is time consuming, since we have to trace the segment each time to compare it with another segment.

There is an even easier way to compare the lengths of two or more line segments with the help of a ruler. A ruler lo…

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