 Let's say we wanted to compare line segments. So if I draw a line segment like this a be and Another one like this and if I ask which one is larger is a be larger or pq larger and There are many ways to identify or answer this question I know what you're thinking you can clearly see that a be is larger than pq But imagine if I draw something like this and if I name it x y and then I ask which one is larger now Probably there would be doubts whether x y is larger or a be is larger And in fact I could still draw two equal segments and there wouldn't be confirmed way to know whether the two segments are equal or not So what are different ways in which we can actually confirm whether the length of two line segments is equal or not? Or which one is larger just pause the video for once and think about all the ways in which you can identify this Think about all the tools that you have in your compass box or think about Anything that your teacher might have used when I had drawn a be and pq at segments The first thing that we did was observation the simple observation That you did and you were able to answer that a be was in fact larger Let me write segment a be was in fact larger than segment pq So observation is a very first method in which you can compare two line segments But would observation work all the time as soon as I had drawn x y as a segment when we had x y and a be We couldn't tell with confidence which segment was larger and so the limitation for eyes Is that it cannot identify my new differences do they they don't and that's why Observation doesn't work all the time I would say it doesn't work most of the time because the instrument that we are relying upon is our eyes Right the other interesting method through which you can compare line segments is by tracing So there is something called trace paper. So what we usually do is that when whenever we want to draw something So, let's say there is this segment a be given to us we put a tracing paper over a be and Because this tracing paper is semi transparent this a be looks a little blurred I am showing it using dotted lines and then you can draw the required segment over a be so start from a Then you would you would want to draw another segment and let's say this was pq And then you would definitely know pq whatever that you've drawn is less than a be but what are the disadvantages of this particular trace paper method is that you have to draw pq if a be and pq were given to you like that There would be another problem of transferring or drawing pq over the trace paper if you didn't know the length of pq And if you didn't have any other instrument to measure or compare the line segments So trace paper only works in theory It's not very practical and that's why first is observation and next method is tracing or using a trace paper Which have clear disadvantages? I know what you're thinking many students or many viewers might have thought about using a ruler I know so if you measure the length of the line segment using a ruler You can compare the length very quickly and that method really works well and I am going to discuss the disadvantage So you put one end of a line segment at 0 centimeter. So just pardon my drawing here I'm not being too accurate and neither I am keeping the ruler or the segments parallel But just let's just assume for this example that these things are parallel So let's say this is a and this is b and this is You measure it and you say this is 8 centimeters And then then you write it down here since I'm not going to move the ruler I'll just quickly write the measurement of a b and let's say the other segment was Like this and then you know this is pq and pq is 6 centimeters And then you clearly know a b is greater than 6 centimeter But what if we were measuring length of x y and we know from the start x y was close to a b Let's say this was the length of x y and we can clearly see Here that length of x y is close to 8 centimeter But we cannot be sure again because there is a difference of 1 millimeter here Note that 10 millimeters which is shown as mm is equal to 1 centimeter So here there is little difference and there is another error that we humans do when we measure through rulers is known as parallax error The description of this is that how you look at the measurement greatly affects the measurement that you see You have to be looking exactly from above and you have to be looking exactly from above To have the confirmed or to be sure of the observation or the reading that you've taken So even if I can say that x y is little Below 8 centimeter or probably about 7.9 centimeter There is a disadvantage known as parallax error when we are looking From different angles at the ruler So is there any foolproof method to this there in fact is and you have to use a divider with the ruler So let's say we have two segments again a b And let's just draw this x y and how do we compare that using the ruler and a divider divider looks like this so it has two arms like this and there is a pointy end At both arms and you can rotate this divider and put these two ends at the ends of x y or a b And the distance between the ends remains the same in that case So once you measure a b what you have to do is that you have to keep the keep one end of the divider here and other end at b And now by keeping the same setting of the divider Keep one end at x and see if the other end fits at y or not If it falls below then of course a b would be less than x y and if it goes beyond y then a b would be greater than y So this is a simple method in which you can find Which one is larger, but how do you find exact length? Then you have to keep the divider at the end Here of the ruler measure both the lens through any angle Then it would have reduced the parallax error since the distance between the arms is not going to change As per through which angle you're looking at it So using divider is a very good method to compare lens and I encourage you to use all the four methods discussed here In order to compare different line segments