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

Cross-posted from here.

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Question

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

1. yes, the segment addition postulate is a more specific case of the partition postulate, and
2. 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:

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

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