Reverse triangle inequality states that the length of any side of the triangle is greater than the difference between the remaining two sides. Triangle inequality states that the sum of the lengths of two sides of the triangle is greater than, or equal to, the length of the remaining side.
Euclid proved the triangle inequality for distances in plane geometry. In a right-angled triangle, the length of the longest side, or hypotenuse, is greater than the length of the other two sides but is less than their sum. Triangle inequality is a defining property of norms and measures of distance.