Comparison Of Two Line Segments

Comparison of Two Line Segments

By comparison of line segments we mean which of them is longer or shorter. Thus, by comparison of line segments we mean an order relation between their lengths.

(i) Comparison by observation:

In the figure (i) we can easily make out AB  is shorter than CD but in figure (ii) and figure (iii) it is difficult to compare them. Hence, this kind of comparison is not always possible as our eyes cannot catch the minute difference in the lengths of the segments. Thus, we use instruments from a regular geometry box.

(ii) Comparison by tracing:

(iii) Comparison of Line Segments Using Divider

A divider is an instrument having two legs with pointed metal ends.

In order to compare two line segments AB and CD, we place the end-point of one arm of the divider at A and open the arms carefully so that the end-point of the other arm is at B as shown in figure (i) given below

Now we lift the divider and without disturbing its opening, place the end-points of one arm of C and the end-point of the other arm on the segment CD. There are three possibilities.

Case I: When the end point of the second arm falls on D; In this case, we say that the segments AB and CD are equal and we write AB = CD [Figure (ii)]

Case II: When the end point of the second arm falls between C and D, in this case, we  say that the segment AB is smaller than or less then the segment CD and we write AB < CD [Figure (iii)]

Case III: When the end-point of the second arm falls outside CD; In this case, we say that the segment AB is greater than or larger than the segment CD and we write AB > CD [Figure (iv)]

Congruent Segments 

Two segments having the same length are called congruent segments

Measuring Line Segments With A graduated Ruler

To measure the length of line segment AB, we place the ruler with its graduated edge along AB such that zero mark (0) of the ruler coincides with the point A.

Measuring The length of a line segment using the divider

To measure the length of a line segment AB with divider we place the end points of divider on A and B. Then gently place the one end of divider on zero and the other pointed end falls on some mark.

Constructing a line segment of given length

(i) Using Ruler

To draw PQ = 4.8 cm.

Constructing A line segment of Given length with compass

Suppose we are required to construct a segment of 5.3 cm. Draw a line on a sheet of paper. Mark a point A on it. Take the compasses and place its pointed metal end on the zero mark of the graduated ruler. Open the compasses without disturbing its legs. Place its pointed metal end on the point A on the line. Keeping it on A, mark the point B with the point of the pencil. Then we get the line segment AB of 5.3 cm.