High Quality Content by WIKIPEDIA articles! In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. In Euclidean geometry and some other geometries this is a theorem. In the Euclidean case, in both the less than or equal to and greater than or equal to statements, equality occurs only if the triangle has a 180° angle and two 0° angles, as shown in the bottom example in the image to the right. The inequality can be viewed intuitively in either R2 or R3. The figure at the right shows two examples. The triangle inequality is a theorem in spaces such as the real numbers, all Euclidean spaces, the Lp spaces (p ? 1), and any inner product space.

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