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In geometry, the segment addition postulate states that given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC. This is related to the triangle inequality, which states that \( AB + BC \geq AC \) with equality if and only if A, B, and C are 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 of segments.

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Mathematics Encyclopedia

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