Segment Addition Postulate (SAP)
If B is between A and C, then AB + BC = AC
The Segment Addition Postulate (SAP) is a fundamental geometric concept that states that given three points on a line segment, the middle point will always divide the line segment into two smaller segments with lengths that are proportional to each other. In other words, if we have a line segment AB, and a point C lies in between A and B, then according to the SAP, the length of AC added to the length of CB will be equal to the length of AB. This is mathematically represented as
AC + CB = AB
The Segment Addition Postulate can also be used to find the measure of a line segment when its endpoints and the measure of one of its smaller segments are given. We can use the proportional relationship given by SAP to set up an equation and solve for the unknown length. For example, if we know that AC has a length of 7 units, and AB has a length of 15 units, and we want to find the length of CB, we can set up the following equation using the SAP:
AC + CB = AB
7 + CB = 15
CB = 8 units
Therefore, we can conclude that CB has a length of 8 units based on the SAP.
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