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





            Each centimetre is divided into 10 millimetres. So, 1 mm is 0.1 cm, 2 mm is 0.2 cm, and so on.
            2.4 cm will mean 2 cm and 4 mm.

            Let us measure a line segment, say AB, using a ruler.
                     A                                  B







            We place the ruler along the line
            segment AB , such that the zero mark
            of the ruler coincides with point A.
            We read the mark on the ruler that
            coincides with point B. It lies along
            the second division after the 6 cm
            marking.
            Hence, the length of  AB  is 6 cm
            2 mm, or 6.2 cm.
            However, there is a chance for errors in this procedure. The thickness of the ruler may cause
            difficulties in reading it. Errors can also happen due to angular viewing.
            Hence, for correct measurement, the eye should be positioned just vertically above the mark.

            We can avoid such errors by using a divider.
            To get the accurate length of line segment AB  using a divider and ruler, we open the divider and
            place the tips of its arms on the end points A and B of the line segment.
                                           Now, we place the divider without disturbing its opening on the ruler,
                                           so that the tip of its one arm coincides with the zero mark.







            A                        B









            Then, we read the mark against the tip of other arm of the divider.
            This is the length of line segment AB. Clearly, the length of AB  = 4.4 cm.

            Example 5: If A, B, and C are three points on a line
            such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which               Quick Check
            one of them lies between the other two?
            Solution: We have AB + BC = 5 cm + 3 cm = 8 cm = AC            Draw any line segment, say  PQ . Take any
                                                                           point R lying in between P and Q. Measure the
                             5 cm                   3 cm
                 A                           B                C            lengths of PQ , PR  and QR .
            It means B lies between A and C.                               Is PQ  = PR  + QR ?


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