Ruler Postulate and the Segment Addition Post

Welcome to a lesson on the ruler postulate and the segment edition postulate. The goals are to use the ruler postulate to determine a length and also to illustrate this segment addition postulate. The ruler postulate states a distance between two points is the absolute value of the difference between the real numbers shown on a ruler. So for example, looking at the centimeter side of a ruler, if we want to know the distance from 8 to 23. We just need to determine the absolute value of the difference between 8 and 23. And notice it doesn't specify an order so we can take the absolute value of 23 -8, or take the absolute value of 8 -23. Well, 23 -8 is going to give us 15, and the absolute value of 15 is 15. And 8 -23 is going to give us negative 15, but the absolute value of negative 15 is still positive 15. So regardless of the order of the subtraction, because we're taking the absolute value, it will always be positive. And that's good because distance is always positive. If you live 5 miles from school, and you ride the bus from your house to school, it would be 5 miles, and when you ride the bus from school to home, it's still 5 miles. So regardless of the direction, the distance will be positive. The segment addition postulate tells us that if we have the segment AC and the point B is between point a and point C, then the length of AB plus the length of BC must equal the length of AC. So the distance from a to B added to the distance from B to C would give us the total length from point a to point C looking at a numerically, if we know the segment AC has a length of, let's say, 15 centimeters, and we place the point B between points a and C on the segment. So the length of segment AB would be four, and the length of segment BC would be 11, so from this postulate, AB would be four, BC would be 11, and so AB plus BC would equal AC, which is equal to 15. And that's the segment addition postulate. Thank you for watching.