Learn about Measuring Segments In this lesson, let’s learn how to measure segments. So what we will learn is how do we measure line segments. And the way we do that before we get to the two problems given to us, if we have a line segment AB, it starts here and it ends here, the measurement of this line segment, the length of the measurement of this can be simply computed by looking at the absolute value of A minus B, which is the value of A on the number line and the value of B on the number line. Let’s actually use capital letters for both. So we can calculate the absolute value, or it could be B minus Al; it does not make a difference. Since we are computing the absolute value anyway, A minus B and B minus A will remain the same. Let’s actually use a couple of problems, so let’s try this. We need to find the length of the segment DC, so that’s D and C. So what have we learned? What we have to do is find the absolute value of D minus C or absolute value of C minus D. What is D minus C? Well, D is at 4.5 and C is 1, so 4.5 – 1 = 3.5. Absolute value of 3.5 equals 3.5. Let’s do it this way, C minus D. What is C? C is 1 minus—what is D? 4.5. 1 – 4.5 = -3.5, absolute value of -3.5 is 3.5. So what’s the length of this segment? 3.5. All we did was take the two points, plug in their values and subtract them and make sure we take only the positive. Whatever the number is, take the positive value of it. Let’s do it again for a different problem. In this case, we have to measure the length of the segment XY and XZ. Let’s do XY first. So X minus Y, absolute value is what we need. What is X? X is 1. What is Y? Y is 6. So 1 – 6 = -5, absolute value of that is 5. So that’s the length of XY. Length of XZ, which is this one, is X minus Z. What is X? X is still 1. What is Z? Z is -4. What is 1 + 4? It equals 5, minus and minus, subtraction of a negative number is the same as adding the number. 1 + 4 = 5. What’s the absolute value of 5? 5. So length of XY is equal to length of XZ. These are called congruent lines because they are exactly the same size. And the way you represent two lines of the same size is you put ticks in them, so XY, XZ, if we put a single tick mark, a single check mark, these means these lines are of the same size or congruent. So yes, are these segments congruent? Yes, the two segments XY and XZ are indeed congruent.