# Q&A: Why are the Segment Addition Postulate and the Partition Postulate Two Different Things?

*Cross-posted from here.*

I could be wrong but those two ideas sound the same, just that the partition postulate is more general.

*Segment Addition Postulate:* If three points A, B, and C are collinear such that B lies between A and C, then the sum of the lengths of segment AB and segment BC is equal to the length of the entire segment AC.

*Partition Postulate:* The whole is equal to the sum of its parts.

## Answer

Without going down into the rabbit hole of axiomatic systems, I think the high-level answer you’re looking for is that

- yes, the segment addition postulate is a more specific case of the partition postulate, and
- the reason why a geometry course might present both postulates is that the segment addition postulate clarifies what is meant in a case where the partition postulate is vague enough to lead to ambiguity.

To elaborate on item 2 – it could be tempting to claim that the partition postulate supports the following statement, which is not true in general:

*Given three points A, B, and C, the sum of the lengths of segment AB and segment BC is equal to the length of the entire segment AC.*

The segment addition postulate specifies the additional conditions that are required for the statement to hold true in general:

*Given three***collinear**points A, B, and C**such that B lies between A and C**, the sum of the lengths of segment AB and segment BC is equal to the length of the entire segment AC.