# triangle inequality

- the theorem that the absolute value of the sum of two quantities is less than or equal to the sum of the absolute values of the quantities.
- the related theorem that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors.
- (for metric spaces) the related theorem that the distance between two points does not exceed the sum of their distances from any third point.

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## Origin of triangle inequality^{}

First recorded in 1960–65

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018