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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

By using observation, we cannot say which one is longer and which one is shorter. In such
situations, we need a better way for comparison.

Now, we first trace one of the two line segments, say ‘AB ’, on a piece of tracing paper and place
it on the other one, i.e., PQ such that point A coincides with point P. Observe the position of
another point B.

There are three possibilities that may occur in doing so:
P Q
(i) If B lies between P and Q, it means AB < PQ .
A B

(ii) P Q If B lies beyond Q, it means AB > PQ .
A B
P Q
(iii) If B coincides with Q, it means AB = PQ .
A B
This method depends upon the accuracy of tracing the line segment.
Moreover, if we want to compare with another length, we have to trace that line segment. This
can be difficult and time-consuming to trace the lengths every time. Therefore, we use a divider
to compare them.
Comparison Using a Divider

Do you recognise all the items given in an instrument box?

Among all the instruments, one is shown here in the alongside picture.
This instrument is called a divider. As we can see, it has two arms joined together with
the help of a knob at one end. The other two ends of the arms have metallic needles.

Let us compare the lengths of two line segments using it. Divider
Consider the two line segments given alongside. P Q R S

To compare PQ and RS, we place the endpoint of one arm of the
divider at P, then open the divider so that the endpoint of the other
arm lies on Q (see figure). After that, we lift the divider and without
disturbing its opening, place the metallic end of one arm at R. Now,
check whether the metallic end of other arm falls on S or not.

There are three possibilities that may occur in doing so:
(a) PQ > RS , if the other end lies beyond the S.
P Q R S
(b) PQ = RS , if the other end lies exactly at S.
(c) PQ < RS , if the other end lies between R and S.

Measuring a Line Segment

To measure the length of a line segment, we use a ruler. Have you noticed the markings along the
edges of the ruler? If not, have a look at the picture of the ruler given below.

One edge is marked in centimetres and millimetres, and the other edge is marked in inches.

33 Lines and Angles