# Segment addition postulate

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{{Short description|Postulate in geometry}}
{{Multiple issues|
{{No footnotes|date=November 2021}}
{{One source|date=November 2024}}
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In [geometry](/source/geometry), the '''segment addition postulate''' states that given 2 [point](/source/Point_(geometry))s A and C, a third point B lies on the [line segment](/source/line_segment) AC [if and only if](/source/if_and_only_if) the [distance](/source/distance)s between the points satisfy the [equation](/source/equation) AB + BC = AC. This is related to the [triangle inequality](/source/triangle_inequality), which states that AB + BC <math>\geq</math> AC with equality if and only if A, B, and C are [collinear](/source/collinear) (on the same line). This in turn is equivalent to the proposition that the shortest distance between two points lies on a straight line.

The segment addition postulate is often useful in proving results on the [congruence](/source/Congruence_(geometry)) of segments.

==External links==
* https://www.course-notes.org/Geometry/Segments_and_Rays/Segment_Addition_Postulate

Segment Addition Calculator:
* https://www.omnicalculator.com/math/segment-addition-postulate

Category:Logic
Category:Elementary geometry

{{elementary-geometry-stub}}

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Adapted from the Wikipedia article [Segment addition postulate](https://en.wikipedia.org/wiki/Segment_addition_postulate) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Segment_addition_postulate?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.